4t ESO/4.05 INEQUACIONS/4.05.2 Signe d'una expressió algèbrica 4.05.2.10 TEORIA: INEQUACIO INTERVAL

Interval → Inequació
Expressió	interval	inequació
Nombres més petits o iguals que 4	(-∞,4]	x≤4
Nombres més grans que -2	(-2,+∞)	x>-2
Nombres entre -2 (inclòs) i 4	[-2,4)	«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8805;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8743;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§lt;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»4«/mn»«/mstyle»«/math»
Nombres més petits que -2 i més grans que 4	(-∞,-2)U(4,+∞)	«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§lt;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8744;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#62;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»4«/mn»«/mrow»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 4.05.2.11 Interval a inequació x sup a Escriu en forma d'inequacions, l'interval

]]> La resposta és #sol

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mfenced><mrow><cn>-∞</cn><mo>,</mo><mi>a1</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>x</mi><mo><</mo><mi>a1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> a]]> Escriu en forma d'inequacions, l'interval

]]> La resposta és #sol

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mfenced><mrow><mi>a1</mi><mo>,</mo><cn>+∞</cn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>x</mi><mo>></mo><mi>a1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 4.05.2.13Interval a inequació entre 2 nombres Escriu en forma d'inequacions, l'interval

]]> La resposta és #sol

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a1</mi><mo><</mo><mi>a2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mfenced><mrow><mi>a1</mi><mo>,</mo><mi>a2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resol_inequació</mi><mfenced><mrow><mi>a1</mi><mo><</mo><mi>x</mi><mo>∧</mo><mi>x</mi><mo><</mo><mi>a2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>a1</mi><mo><</mo><mi>x</mi><mo><</mo><mi>a2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mo>-</mo><mn>6</mn><mo>∧</mo><mi>x</mi><mo><</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo><</mo><mi>x</mi><mo><</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'interval conté tots els nombres entre #a1 i #a2, per tant, els nombres x de l'interval són més grans que #a1 i més petits que #a2.

]]> 4.05.2.14 Interval a inequació fora 2 nombres Escriu en forma d'inequacions, l'interval

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8746;«/mo»«mfenced mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/math»

]]> La resposta és #sol

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a1</mi><mo><</mo><mi>a2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mfenced><mrow><cn>-∞</cn><mo>,</mo><mi>a1</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfenced><mrow><mi>a2</mi><mo>,</mo><cn>+∞</cn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resol_inequació</mi><mfenced><mrow><mi>a1</mi><mo>></mo><mi>x</mi><mo>∨</mo><mi>x</mi><mo>></mo><mi>a2</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><cn>-∞</cn><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><cn>+∞</cn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>3</mn><mo>∨</mo><mi>x</mi><mo><</mo><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 4.05.2.20 TEORIA: SigneExpressió1rGrau

Signe de ax + b
x	.oo	-b/a	+oo
ax+b	Signe contrari de a	0	Signe de a

]]> 0.0000000 0.0000000 0 Resol: #e #v 0

Format de la resposta: x<-2/5 (SIMPLIFICADA)

]]> #e #v 0 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«/math» #sol

]]> 1.0000000 0.5000000 0 0 #sol

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/math»

Després cal fer la taula de signes.

]]> La taula de signes mostra que:

pels valors de x inferiors a #s, l'expressió és #m_1 (#n_1 #a)
pels valors de x superiors a #s, l'expressió és #m_2 (#n_2 #a)

x	«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»§#8734;«/mo»«/math»	#s	«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»+«/mo»«mo»§#8734;«/mo»«/math»
#e	#s_1	0	#s_2

]]> 4.05.2.22Q Resoldre ax+bSUP0 (a NEGATIU) Resol: #e #v 0

Format de la resposta: x<-2/5 (SIMPLIFICADA)

]]> #e #v 0 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«/math» #sol

]]> 1.0000000 0.5000000 0 0 #sol

Després cal fer la taula de signes.

]]> La taula de signes mostra que:

pels valors de x inferiors a #s, l'expressió és #m_1 (#n_1 #a)
pels valors de x superiors a #s, l'expressió és #m_2 (#n_2 #a)

x	«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»§#8734;«/mo»«/math»	#s	«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»+«/mo»«mo»§#8734;«/mo»«/math»
#e	#s_1	0	#s_2

]]> 4.05.2.31Q Resoldre ax+bALEATORISUP0 (a ALEATORI) Resol: #e #v 0

Format de la resposta: x<-2/5 (SIMPLIFICADA)

]]> 1.0000000 0.3333333 0 0 #sol

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mo><</mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>></mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>⩽</mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>⩾</mo><mo>"</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mo>-</mo><mi>b</mi><mo>/</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>"</mo><mo>></mo><mo>"</mo></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>x</mi><mo>></mo><mi>s</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>"</mo><mo><</mo><mo>"</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mi>x</mi><mo><</mo><mi>s</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>"</mo><mo>⩽</mo><mo>"</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mi>x</mi><mo>⩽</mo><mi>s</mi></mrow><mrow><mi>sol</mi><mo>=</mo><mi>x</mi><mo>⩾</mo><mi>s</mi></mrow></apply></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>m_2</mi><mo>=</mo><mo>"</mo><mi>positiva</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mo>"</mo><mi>signe</mi><mo> </mo><mi>de</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>m_1</mi><mo>=</mo><mo>"</mo><mi>negativa</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>n_1</mi><mo>=</mo><mo>"</mo><mi>signe</mi><mo> </mo><mi>contrari</mi><mo> </mo><mi>de</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>s_1</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s_2</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>"</mo><mo>></mo><mo>"</mo></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>x</mi><mo><</mo><mi>s</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>"</mo><mo><</mo><mo>"</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mi>x</mi><mo>></mo><mi>s</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>"</mo><mo>⩽</mo><mo>"</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mi>x</mi><mo>⩾</mo><mi>s</mi></mrow><mrow><mi>sol</mi><mo>=</mo><mi>x</mi><mo>⩽</mo><mi>s</mi></mrow></apply></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>m_2</mi><mo>=</mo><mo>"</mo><mi>negativa</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mo>"</mo><mi>signe</mi><mo> </mo><mi>de</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>m_1</mi><mo>=</mo><mo>"</mo><mi>positiva</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>n_1</mi><mo>=</mo><mo>"</mo><mi>signe</mi><mo> </mo><mi>contrari</mi><mo> </mo><mi>de</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>s_1</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s_2</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⩽</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mfrac><mn>7</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiva</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negativa</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>contrari</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer cal resoldre:

Després cal fer la taula de signes.

]]> La taula de signes mostra que:

pels valors de x inferiors a #s, l'expressió és #m_1 (#n_1 #a)
pels valors de x superiors a #s, l'expressió és #m_2 (#n_2 #a)

x	«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»§#8734;«/mo»«/math»	#s	«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»+«/mo»«mo»§#8734;«/mo»«/math»
#e	#s_1	0	#s_2

]]> 4.05.2.40 TEORIA: SIGNEPOL G2 TAULA

Signe de ax² + bx + c
Si no té solució, té el signe de a. Si té solució doble, té el signe de a excepte en x₁. Si té dues solucions, x₁ i x₂:
x	.oo	x₁		x₂	+oo
ax²+bx+c	Signe de a	0	Contrari de a	0	Signe de a

]]> 0.0000000 0.0000000 0 4.05.2.41Q Resol ax^2+bx+c Negatiu Resol: #e < 0

Format de la resposta:

Entre dos nombres: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#8743;«/mo»«mi»x«/mi»«mo»§lt;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8743;«/mo»«mo»=«/mo»«mi»i«/mi»«mo»)«/mo»«/math»

Altra situació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§lt;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#8744;«/mo»«mi»x«/mi»«mo»§#62;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8744;«/mo»«mo»=«/mo»«mi»o«/mi»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>x_1</mi><mo><</mo><mi>x_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_2</mi><mo>)</mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mfenced><mrow><mi>x_1</mi><mo>+</mo><mi>x_2</mi></mrow></mfenced></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><mi>x_1</mi><mo>*</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>e</mi><mo><</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>e1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mo>{</mo><mi>t_1</mi><mo>,</mo><mi>t_2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi><mo>=</mo><mo>{</mo><mi>t_2</mi><mo>,</mo><mi>t_1</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiu</ms><mo>,</mo><ms>positiu</ms><mo>,</mo><ms>negatiu</ms><mo>,</mo><mo>+</mo><mo>,</mo><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>48</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mo>-</mo><mn>6</mn><mo>∧</mo><mi>x</mi><mo><</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>></mo><mo>-</mo><mn>6</mn><mo>,</mo><mi>x</mi><mo><</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo><</mo><mn>4</mn><mo>,</mo><mi>x</mi><mo>></mo><mo>-</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mo>-</mo><mn>6</mn><mo>∧</mo><mi>x</mi><mo><</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es resol l'equació de 2n grau.

el discriminant és #d i les solucions són #x_1 i #x_2.

(ES COMPROVEN AMB S = #S1 I P = #P1)

Després es fa la taula.

]]> Si fem la taula:

Com que a és #r1,

#e és #r2 (signe de a), #r4, per x<#x_1 o per x>#x_2

#e és #r3 (signe contrari de a), #r5, per #x_1<x i per x<#x_2

.oo

#x_1

#x_2

+oo

#s1

#s2

#s1

]]> 4.05.2.42Q Resol ax^2+bx+c Positiu Resol: #e > 0

Format de la resposta:

]]> #e > 0 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8660;«/mo»«/math» #sol

]]> 1.0000000 0.3333333 0 0 #sol

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xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>></mo><mo>-</mo><mn>6</mn><mo>,</mo><mi>x</mi><mo><</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo><</mo><mn>4</mn><mo>,</mo><mi>x</mi><mo>></mo><mo>-</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mo>-</mo><mn>6</mn><mo>∧</mo><mi>x</mi><mo><</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es resol l'equació de 2n grau.

el discriminant és #d i les solucions són #x_1 i #x_2.

(ES COMPROVEN AMB S = #S1 I P = #P1)

Després es fa la taula.

]]> Si fem la taula:

Com que a és #r1,

#e és #r2 (signe de a), #r4, per x<#x_1 o per x>#x_2

#e és #r3 (signe contrari de a), #r5, per #x_1<x i per x<#x_2

.oo

#x_1

#x_2

+oo

#s1

#s2

#s1

]]> 4.05.2.51Q Resol ax^2+bx+c ALEATORI Resol: #e #v 0

Format de la resposta:

Entre dos nombres: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mn»2«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#8743;«/mo»«mn»5«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8743;«/mo»«mo»=«/mo»«mi»i«/mi»«mo»)«/mo»«/math»

Altres situacions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§lt;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#8744;«/mo»«mi»x«/mi»«mo»§#62;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8744;«/mo»«mo»=«/mo»«mi»o«/mi»«mo»)«/mo»«/math»

]]> #e #v 0 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8660;«/mo»«/math» #sol

]]> 1.0000000 0.3333333 0 0 #sol

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xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>e1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mo>{</mo><mi>t_1</mi><mo>,</mo><mi>t_2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi><mo>=</mo><mo>{</mo><mi>t_2</mi><mo>,</mo><mi>t_1</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>R</mi></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>r1</mi><mo>,</mo><mi>r2</mi><mo>,</mo><mi>r3</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negatiu</ms><mo>,</mo><ms>negatiu</ms><mo>,</mo><ms>positiu</ms><mo>,</mo><mo>-</mo><mo>,</mo><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>45</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>162</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>9</mn><mo>∨</mo><mi>x</mi><mo><</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>></mo><mn>9</mn><mo>,</mo><mi>x</mi><mo><</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo><</mo><mn>6</mn><mo>,</mo><mi>x</mi><mo>></mo><mn>9</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>9</mn><mo>∨</mo><mi>x</mi><mo><</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>,</mo><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>,</mo><mn>54</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es resol l'equació de 2n grau.

el discriminant és #d i les solucions són #x_1 i #x_2.

ES COMPROVEN AMB S = #S1 I P = #P1

Després es fa la taula.

]]> Si fem la taula:

Com que a és #r1,

#e és #r2 (signe de a), #r4, per x<#x_1 o per x>#x_2

#e és #r3 (signe contrari de a), #r5, per #x_1<x i per x<#x_2

.oo

#x_1

#x_2

+oo

#s1

#s2

#s1

]]> 4.05.2.52Q Resol ax^2+bx+c ALEATORI_2 Resol: #e #v 0

Format de la resposta:

]]> #e #v 0 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8660;«/mo»«/math» #sol

]]> 1.0000000 0.3333333 0 0 #sol

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>x_1</mi><mo><</mo><mi>x_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_2</mi><mo>)</mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mfenced><mrow><mi>a</mi><mo>*</mo><mfenced><mrow><mi>x_1</mi><mo>+</mo><mi>x_2</mi></mrow></mfenced></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>*</mo><mi>x_1</mi><mo>*</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mo><</mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>></mo><mo>"</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>"</mo><mo><</mo><mo>"</mo></mrow><mtable><mtr><mtd><mi>e1</mi><mo>=</mo><mi>e</mi><mo><</mo><mn>0</mn></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>"</mo><mi>positiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mo>"</mo><mi>positiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>"</mo><mi>negatiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>r4</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>r5</mi><mo>=</mo><mo>"</mo><mi>i</mi><mo> </mo><mi>és</mi><mo> </mo><mi>el</mi><mo> </mo><mi>que</mi><mo> </mo><mi>demana</mi><mo> </mo><mi>l</mi><mo>'</mo><mi>enunciat</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>"</mo><mi>negatiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mo>"</mo><mi>negatiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>"</mo><mi>positiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>r5</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>r4</mi><mo>=</mo><mo>"</mo><mi>i</mi><mo> </mo><mi>és</mi><mo> </mo><mi>el</mi><mo> </mo><mi>que</mi><mo> </mo><mi>demana</mi><mo> </mo><mi>l</mi><mo>'</mo><mi>enunciat</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></mtd></mtr></mtable><mtable><mtr><mtd><mi>e1</mi><mo>=</mo><mi>e</mi><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>"</mo><mi>positiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mo>"</mo><mi>positiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>"</mo><mi>negatiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>r5</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>r4</mi><mo>=</mo><mo>"</mo><mi>i</mi><mo> </mo><mi>és</mi><mo> </mo><mi>el</mi><mo> </mo><mi>que</mi><mo> </mo><mi>demana</mi><mo> </mo><mi>l</mi><mo>'</mo><mi>enunciat</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>r1</mi><mo>=</mo><mo>"</mo><mi>negatiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mo>"</mo><mi>negatiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>r3</mi><mo>=</mo><mo>"</mo><mi>positiu</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>r4</mi><mo>=</mo><mo>"</mo><mo> </mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>r5</mi><mo>=</mo><mo>"</mo><mi>i</mi><mo> </mo><mi>és</mi><mo> </mo><mi>el</mi><mo> </mo><mi>que</mi><mo> </mo><mi>demana</mi><mo> </mo><mi>l</mi><mo>'</mo><mi>enunciat</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>e1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mo>{</mo><mi>t_1</mi><mo>,</mo><mi>t_2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi><mo>=</mo><mo>{</mo><mi>t_2</mi><mo>,</mo><mi>t_1</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>R</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi><mo>=</mo><mi>x_1</mi><mo>*</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>x_1</mi><mo>,</mo><mi>x_2</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>81</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>r1</mi><mo>,</mo><mi>r2</mi><mo>,</mo><mi>r3</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>s2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negatiu</ms><mo>,</mo><ms>negatiu</ms><mo>,</mo><ms>positiu</ms><mo>,</mo><mo>-</mo><mo>,</mo><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>45</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>162</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>9</mn><mo>∨</mo><mi>x</mi><mo><</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>></mo><mn>9</mn><mo>,</mo><mi>x</mi><mo><</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo><</mo><mn>6</mn><mo>,</mo><mi>x</mi><mo>></mo><mn>9</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>9</mn><mo>∨</mo><mi>x</mi><mo><</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>,</mo><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>,</mo><mn>54</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es resol l'equació de 2n grau.

el discriminant és #d i les solucions són #x_1 i #x_2.

ES COMPROVEN AMB S = #S1 I P = #P1

Després es fa la taula.

]]> Si fem la taula:

Com que a és #r1,

#e és #r2 (signe de a), #r4, per x<#x_1 o per x>#x_2

#e és #r3 (signe contrari de a), #r5, per #x_1<x i per x<#x_2

.oo

#x_1

#x_2

+oo

#s1

#s2

#s1

]]> 4.05.2.60 TEORIA: SIGNE D'UNA FRACCIÓ

Signe d'una fracció

Cal recordar que:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mtable columnalign=¨left¨ rowspacing=¨0¨»«mtr»«mtd»«mfrac»«mo»+«/mo»«mo»+«/mo»«/mfrac»«mo»=«/mo»«mfrac»«mo»-«/mo»«mo»-«/mo»«/mfrac»«mo»=«/mo»«mo»+«/mo»«/mtd»«/mtr»«mtr»«mtd/»«/mtr»«mtr»«mtd»«mfrac»«mo»+«/mo»«mo»-«/mo»«/mfrac»«mo»=«/mo»«mfrac»«mo»-«/mo»«mo»+«/mo»«/mfrac»«mo»=«/mo»«mo»-«/mo»«/mtd»«/mtr»«/mtable»«/math»

]]> 0.0000000 0.0000000 0 4.05.2.61Q SigneFracció ax+b/x+c Aleat_1 Resol: #e #v 0

Format de la resposta:

Entre dos nombres: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mo»§lt;«/mo»«mi»x«/mi»«mo»§#8743;«/mo»«mi»x«/mi»«mo»§lt;«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8743;«/mo»«mo»=«/mo»«mi»i«/mi»«mo»)«/mo»«/math»

Altra situació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§lt;«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#8744;«/mo»«mi»x«/mi»«mo»§#62;«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#8744;«/mo»«mo»=«/mo»«mi»o«/mi»«mo»)«/mo»«/math»

]]> Els intervals solució queden definits per #sol

]]> 1.0000000 0.5000000 0 0 #sol

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>x_1</mi><mo><</mo><mi>x_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mo><</mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>></mo><mo>"</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_1</mi><mo>)</mo></mrow><mrow><mi>x</mi><mo>-</mo><mi>x_2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mi>e</mi><mo><</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><mi>e</mi><mo>></mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable 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definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>m_2</mi><mo>=</mo><mo>"</mo><mi>negativa</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mo>"</mo><mi>signe</mi><mo> </mo><mi>contrari</mi><mo> </mo><mi>de</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>m_1</mi><mo>=</mo><mo>"</mo><mi>positiva</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>n_1</mi><mo>=</mo><mo>"</mo><mi>signe</mi><mo> </mo><mi>de</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>d4</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>d5</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s_1</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s_2</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>m_2</mi><mo>=</mo><mo>"</mo><mi>positiva</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mo>"</mo><mi>signe</mi><mo> </mo><mi>contrari</mi><mo> </mo><mi>de</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>m_1</mi><mo>=</mo><mo>"</mo><mi>negativa</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>n_1</mi><mo>=</mo><mo>"</mo><mi>signe</mi><mo> </mo><mo> </mo><mi>de</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>d4</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>d5</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s_1</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s_2</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>x_1</mi><mo>,</mo><mi>x_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfrac><mo><</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math 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xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>contrari</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sig</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiva</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>2</mn><mo>∧</mo><mi>x</mi><mo><</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="equivalent_equations"/><assertion name="syntax_expression"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal fer la taula de signes per veure que:

pels valors de x inferiors a #x_1, l'expressió és #m_1 (#n_1 #a)
pels valors de x entre #x_1 i #x_2, l'expressió és #m_2 (#n_2 #a)
pels valors de x superiors a #x_2, l'expressió és #m_1 (#n_1 #a)

x	-oo	#x_1		#x_2	+oo
#n	#d3	0	#d4		#d5
#d	#d6		#d7	0	#d8
#e	#s_1	0	#s_2		#s_1

i l'enunciat demana que l'expressió sigui #sig

]]> 4.05.2.62Q SigneFracció ax+b/x+c Aleat_2 Resol: #e #v 0

Format de la resposta:

]]> Els intervals solució queden definits per #sol

]]> 1.0000000 0.5000000 0 0 #sol

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>x_1</mi><mo><</mo><mi>x_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mo><</mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>></mo><mo>"</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>d6</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d7</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d8</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>"</mo><mo><</mo><mo>"</mo></mrow><mrow><mi>sig</mi><mo>=</mo><mo>"</mo><mi>negativa</mi><mo>"</mo></mrow><mrow><mi>sig</mi><mo>=</mo><mo>"</mo><mi>positiva</mi><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resol_inequació</mi><mfenced><mi>e_3</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>x_1</mi><mo>,</mo><mi>x_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfrac><mo><</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>2</mn><mo>∧</mo><mi>x</mi><mo><</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>></mo><mn>2</mn><mo>,</mo><mi>x</mi><mo><</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo><</mo><mn>3</mn><mo>,</mo><mi>x</mi><mo>></mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiva</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negativa</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>contrari</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sig</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiva</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>2</mn><mo>∧</mo><mi>x</mi><mo><</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="equivalent_equations"/><assertion name="syntax_expression"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal fer la taula de signes per veure que:

pels valors de x inferiors a #x_1, l'expressió és #m_1 (#n_1 #a)
pels valors de x entre #x_1 i #x_2, l'expressió és #m_2 (#n_2 #a)
pels valors de x superiors a #x_2, l'expressió és #m_1 (#n_1 #a)

x	-oo	#x_1		#x_2	+oo
#n	#d3	0	#d4		#d5
#d	#d6		#d7	0	#d8
#e	#s_1	0	#s_2		#s_1

i l'enunciat demana que l'expressió sigui #sig

]]> 4.05.2.71Q SigneFracció ax+b/x+c_Aleat (a Aeat) Resol: #e #v 0

Format de la resposta:

Inequació 1 =x<-5

Inequació 2 =x>3

]]> 1.0000000 0.5000000 0 0 Inequació 1=#t_1Inequació2=#t_2]]>

]]> Inequació 1 =#t_2Inequació 2 =#t_1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>x_1</mi><mo><</mo><mi>x_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mo><</mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>></mo><mo>"</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>x_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>x_1</mi><mo>)</mo></mrow><mrow><mi>x</mi><mo>-</mo><mi>x_2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mi>e</mi><mo><</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><mi>e</mi><mo>></mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>e_1</mi><mo>,</mo><mi>e_2</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol_inequació</mi><mo>(</mo><mi>e_3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mo>{</mo><mi>t_1</mi><mo>,</mo><mi>t_2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi><mo>=</mo><mo>{</mo><mi>t_2</mi><mo>,</mo><mi>t_1</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>m_2</mi><mo>=</mo><mo>"</mo><mi>negativa</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mo>"</mo><mi>signe</mi><mo> </mo><mi>contrari</mi><mo> </mo><mi>de</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>m_1</mi><mo>=</mo><mo>"</mo><mi>positiva</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>n_1</mi><mo>=</mo><mo>"</mo><mi>signe</mi><mo> </mo><mi>de</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>d4</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>d5</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s_1</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s_2</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>m_2</mi><mo>=</mo><mo>"</mo><mi>positiva</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mo>"</mo><mi>signe</mi><mo> </mo><mi>contrari</mi><mo> </mo><mi>de</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>m_1</mi><mo>=</mo><mo>"</mo><mi>negativa</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>n_1</mi><mo>=</mo><mo>"</mo><mi>signe</mi><mo> </mo><mo> </mo><mi>de</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>d4</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>d5</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s_1</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mtd></mtr><mtr><mtd><mi>s_2</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d6</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d7</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d8</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>"</mo><mo><</mo><mo>"</mo></mrow><mrow><mi>sig</mi><mo>=</mo><mo>"</mo><mi>negativa</mi><mo>"</mo></mrow><mrow><mi>sig</mi><mo>=</mo><mo>"</mo><mi>positiva</mi><mo>"</mo></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>x_1</mi><mo>,</mo><mi>x_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>18</mn></mrow><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfrac><mo><</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>5</mn><mo>∨</mo><mi>x</mi><mo><</mo><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>></mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo><</mo><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>></mo><mn>5</mn><mo>,</mo><mi>x</mi><mo><</mo><mo>-</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo><</mo><mo>-</mo><mn>6</mn><mo>,</mo><mi>x</mi><mo>></mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negativa</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>positiva</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>signe</ms><mo> </mo><ms>contrari</ms><mo> </mo><ms>de</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sig</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>negativa</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mo> </mo><mn>1</mn><mo>=</mo><mo>#</mo><mi>t</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>I</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mn>2</mn><mo>=</mo><mo>#</mo><mi>t</mi><mi>_</mi><mn>2</mn></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo>#</mo><mi>t</mi><mi>_</mi><mn>2</mn><mspace linebreak="newline"/><mi>I</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo>#</mo><mi>t</mi><mi>_</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic" correctAnswer="1"/><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Cal fer la taula de signes per veure que:

pels valors de x inferiors a #x_1, l'expressió és #m_1 (#n_1 #a)
pels valors de x entre #x_1 i #x_2, l'expressió és #m_2 (#n_2 #a)
pels valors de x superiors a #x_2, l'expressió és #m_1 (#n_1 #a)

x	-oo	#x_1		#x_2	+oo
#n	#d3	0	#d4		#d5
#d	#d6		#d7	0	#d8
#e	#s_1	0	#s_2		#s_1

i l'enunciat demana que l'expressió sigui #sig

]]> 4.05.2.72Q SigneFracció ax+b/x+c_Aleat (a Aleat)_2 Resol: #e #v 0

Format de la resposta:

Inequació 1 =x<-5

Inequació 2 =x>3

]]> 1.0000000 0.5000000 0 0 Inequació 1=#t_1Inequació2=#t_2]]>

pels valors de x inferiors a #x_1, l'expressió és #m_1 (#n_1 #a)
pels valors de x entre #x_1 i #x_2, l'expressió és #m_2 (#n_2 #a)
pels valors de x superiors a #x_2, l'expressió és #m_1 (#n_1 #a)

x	-oo	#x_1		#x_2	+oo
#n	#d3	0	#d4		#d5
#d	#d6		#d7	0	#d8
#e	#s_1	0	#s_2		#s_1

i l'enunciat demana que l'expressió sigui #sig

]]>