Standard für Fachoberschule /Gleichungen höheren Grades 3. Grad 11 Löse folgende Gleichung:

#a=0

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>64</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>4</mn></mtd></mtr></mtable></mfenced></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"><mo>#</mo><mi>b</mi></math>]]></correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 3. Grad 12 Löse folgende Gleichung:

#a=0

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn></mtd></mtr></mtable></mfenced></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"><mo>#</mo><mi>b</mi></math>]]></correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 3. Grad 21 Löse folgende Gleichung:

#a=0

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>48</mn><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>6</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>8</mn></mtd></mtr></mtable></mfenced></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"><mo>#</mo><mi>b</mi></math>]]></correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 3. Grad 22 Löse folgende Gleichung:

#a=0

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mfrac><mn>4</mn><mn>6</mn></mfrac><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>,</mo><msqrt><mn>2</mn></msqrt></mtd></mtr></mtable></mfenced></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"><mo>#</mo><mi>b</mi></math>]]></correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 3. Grad 23 Löse folgende Gleichung:

#a=0

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>6</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></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"><mo>#</mo><mi>b</mi></math>]]></correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 3. Grad 24 Löse folgende Gleichung:

#a=0

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></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"><mo>#</mo><mi>b</mi></math>]]></correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 3. Grad 31 Löse folgende Gleichung:

#a=0

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>17</mn><mi>x</mi><mo>-</mo><mn>15</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></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"><mo>#</mo><mi>b</mi></math>]]></correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 3. Grad 32 Löse folgende Gleichung:

#a=0

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>8</mn><mi>x</mi><mo>+</mo><mn>12</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> 3. Grad 33 Löse folgende Gleichung:

#a=0

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfrac><mn>11</mn><mn>2</mn></mfrac><mi>x</mi><mo>+</mo><mfrac><mn>15</mn><mn>8</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></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"><mo>#</mo><mi>b</mi></math>]]></correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 3. Grad 34 Löse folgende Gleichung:

#a=0

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>-</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></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"><mo>#</mo><mi>b</mi></math>]]></correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Nullstellen Polynome 1 Bestimme alle Nullstellen der Funktion «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»4«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«msup»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«/math»

]]> 1.0000000 0.3333333 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»4«/mn»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»3«/mn»«/math»

]]> x = 4

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»4«/mn»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»3«/mn»«mo»§#160;«/mo»«/math»(doppelte Nullstelle)

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»4«/mn»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»3«/mn»«/math» (doppelte Nullstelle)

]]> x = -3

]]> Nullstellen Polynome 2 Bestimme alle Nullstellen der Funktion «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mn»3«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»6«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»24«/mn»«mi»x«/mi»«/math»

]]> 1.0000000 0.3333333 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»3«/mn»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»0«/mn»«/math»

]]> x = 0

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»3«/mn»«/msub»«mo»=«/mo»«mn»3«/mn»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»4«/mn»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»3«/mn»«/msub»«mo»=«/mo»«mn»2«/mn»«/math»

]]> Nullstellen Polynome 3 Bestimme alle Nullstellen der Funktion «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfenced»«mrow»«mi»x«/mi»«mo»+«/mo»«mn»5«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»1«/mn»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»3«/mn»«/msub»«mo»=«/mo»«mn»1«/mn»«/math»

]]> x = -5

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«mo»§#160;«/mo»«/math»(doppelte Nullstelle)

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»5«/mn»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»1«/mn»«/math» (doppelte Nullstelle)

]]> x = 5

]]> Nullstellen Polynome 4 Bestimme alle Nullstellen der Funktion «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»x«/mi»«mn»4«/mn»«/msup»«mo»+«/mo»«mn»2«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»3«/mn»«/math»

]]> 1.0000000 0.3333333 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«mo»§#160;«/mo»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»3«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»3«/mn»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»3«/mn»«/msub»«mo»=«/mo»«msqrt»«mn»3«/mn»«/msqrt»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»4«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»1«/mn»«mo»§#160;«/mo»«/math» (doppelte Nullstelle)

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»3«/mn»«/math»

]]> keine der vorgegebenen Lösungen sind richtig

]]> Nullstellen Polynome 5 Bestimme alle Nullstellen der Funktion «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mn»8«/mn»«/math»

]]> 1.0000000 0.3333333 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»3«/mn»«/msub»«mo»=«/mo»«mn»2«/mn»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»4«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»3«/mn»«/msub»«mo»=«/mo»«mn»5«/mn»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»1«/mn»«/math» (doppelte Nullstelle)

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»2«/mn»«/math»

]]> keine der vorgegebenen Lösungen sind richtig

]]> Nullstellen Polynome 6 Bestimme alle Nullstellen der Funktion «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mn»3«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»8«/mn»«mi»x«/mi»«/math»

]]> 1.0000000 0.3333333 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mfrac»«mn»8«/mn»«mn»3«/mn»«/mfrac»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»0«/mn»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mfrac»«mn»8«/mn»«mn»3«/mn»«/mfrac»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mfrac»«mn»8«/mn»«mn»3«/mn»«/mfrac»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mfrac»«mn»8«/mn»«mn»3«/mn»«/mfrac»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»0«/mn»«/math»

]]> keine der vorgegebenen Lösungen sind richtig

]]> Nullstellen Polynome 7 Bestimme alle Nullstellen der Funktion «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»5«/mn»«mi»x«/mi»«mo»-«/mo»«mn»6«/mn»«/math»

]]> 1.0000000 0.3333333 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»6«/mn»«mo»§#160;«/mo»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»6«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«mo»§#160;«/mo»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«/math» (doppelte Nullstelle)

]]> keine der angegebenen Lösungen sind richtig

]]> keine der vorgegebenen Lösungen sind richtig

]]> Nullstellen Polynome 8 Bestimme alle Nullstellen der Funktion «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»9«/mn»«mi»x«/mi»«/math»

]]> 1.0000000 0.3333333 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»3«/mn»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»0«/mn»«/math»

]]> x = 0

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»3«/mn»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»3«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mrow/»«/msub»«mo»=«/mo»«mo»-«/mo»«mn»3«/mn»«/math»

]]> die Funktion besitzt keine Nullstellen

]]> Nullstellen Polynome 9 Bestimme alle Nullstellen der Funktion «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»4«/mn»«/msup»«mo»-«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mfrac»«mn»3«/mn»«mn»2«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/math»

]]> 1.0000000 0.3333333 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«msqrt»«mn»10«/mn»«/msqrt»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«msqrt»«mn»10«/mn»«/msqrt»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«msqrt»«mn»10«/mn»«/msqrt»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»2«/mn»«mo»§#160;«/mo»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«msqrt»«mn»10«/mn»«/msqrt»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«msqrt»«mn»10«/mn»«/msqrt»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»3«/mn»«/msub»«mo»=«/mo»«mn»2«/mn»«/math» 

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mn»1«/mn»«/msub»«mo»=«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»2«/mn»«/msub»«mo»=«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»3«/mn»«/msub»«mo»=«/mo»«mo»-«/mo»«msqrt»«mn»10«/mn»«/msqrt»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi»x«/mi»«mn»4«/mn»«/msub»«mo»=«/mo»«msqrt»«mn»10«/mn»«/msqrt»«/math»

]]> Polynome Schnittpunkte 1 Bestimme die Koordinaten der gemeinsamen Schnittpunkt folgender 2 Funktionen:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»f«/mi»«mn»1«/mn»«/msub»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mn»2«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»+«/mo»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«mo»§#160;«/mo»«mi»u«/mi»«mi»n«/mi»«mi»d«/mi»«mo»§#160;«/mo»«msub»«mi»f«/mi»«mn»2«/mn»«/msub»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»2«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»1«/mn»«/math»

]]> 1.0000000 0.3333333 0 true true abc P (0|1)   Q (-1|-2)

]]> P (0|4)

]]> P (0|1)   Q (-2|-17)

]]> P (2|19)

]]> P (1|0)   Q (0|1

]]> quadratische Gleichungen 11 Löse folgende Gleichung 0= #a

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mo>-</mo><mfrac><mn>9</mn><mn>4</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 12 Löse folgende Gleichung 0= #a

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>13</mn><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mn>52</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 13 Löse folgende Gleichung #a

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>8</mn><mo>,</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 14 Löse folgende Gleichung 0= #a

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mn>16</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 21 Löse folgende Gleichung 0= #a

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>48</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 22 Löse folgende Gleichung #a

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>32</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn></mtd></mtr></mtable></mfenced></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"><mo>#</mo><mi>b</mi></math>]]></correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> quadratische Gleichungen 31 Löse folgende Gleichung 0= #a

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfrac><mn>7</mn><mn>2</mn></mfrac><mi>x</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>4</mn><mo>,</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 32 Löse folgende Gleichung #a

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mi>x</mi><mo>+</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 33 Löse folgende Gleichung #a

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>-</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 34 Löse folgende Gleichung #a

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>-</mo><mn>10</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>10</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 35 Löse folgende Gleichung 0= #a

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>-</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>8</mn><mo>,</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 36 Löse folgende Gleichung 0= #a

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mi>x</mi><mo>+</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 37 Löse folgende Gleichung 0= #a

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfrac><mn>5</mn><mn>3</mn></mfrac><mi>x</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 41 Löse folgende Gleichung:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mfenced»«mrow»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»3«/mn»«mi»x«/mi»«mo»-«/mo»«mn»4«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mn»0«/mn»«/math»

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>4</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 42 Löse folgende Gleichung :

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»10«/mn»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»4«/mn»«/mrow»«/mfenced»«/math»

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>10</mn><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 43 Löse folgende Gleichung:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«mfenced»«mrow»«mi»x«/mi»«mo»+«/mo»«mn»3«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mn»0«/mn»«/math»

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 44 Löse folgende Gleichung:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«msup»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»4«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»1«/mn»«mo»=«/mo»«mn»0«/mn»«/math»

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mn>4</mn></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 45 Löse folgende Gleichung:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«msup»«mfenced»«mrow»«mi»x«/mi»«mo»+«/mo»«mn»3«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»4«/mn»«mo»=«/mo»«mn»0«/mn»«/math»

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>7</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 46 Löse folgende Gleichung :

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«mfenced»«mrow»«mi»x«/mi»«mo»+«/mo»«mn»13«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»13«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mn»0«/mn»«/math»

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mfenced><mrow><mi>x</mi><mo>+</mo><mn>13</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>13</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>13</mn><mo>,</mo><mn>13</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> quadratische Gleichungen 47 Löse folgende Gleichung:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»8«/mn»«/mfrac»«mfenced»«mrow»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mn»4«/mn»«/mrow»«/mfenced»«mo»§#183;«/mo»«mfenced»«mrow»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mn»13«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mn»0«/mn»«/math»

 

]]> 1.0000000 0.0000000 0 0 #b <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><mfenced><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mo>*</mo><mfenced><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>13</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>roots</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mfrac><mn>13</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#b</correctAnswer><correctAnswer id="1"></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Symmetrie 1 Erkenne die Symmetrie am Graphen der Funktion.

#d

]]> 1.0000000 0.3333333 0 true true abc f ist punktsymmetrisch zum Ursprung

]]> f ist punktsymmetrisch zur y-Achse

]]> f ist achsensymmetrisch zum Ursprung

]]> f ist weder symmetrisch zum Ursprung noch zur y-Achse.

]]> f ist achsensymmetrisch zur y-Achse

]]> <question><wirisCasSession><![CDATA[<session lang="de" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>plot</mi><mfenced><mi>f</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plotter1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><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="casSession"/></localData></question> Symmetrie 10 Erkenne die Symmetrie am Graphen der Funktion.

#d

]]> 1.0000000 0.3333333 0 true true abc f ist punktsymmetrisch zum Ursprung

]]> f ist punktsymmetrisch zur y-Achse

]]> f ist achsensymmetrisch zum Ursprung

]]> f ist weder symmetrisch zum Ursprung noch zur y-Achse.

]]> f ist achsensymmetrisch zur y-Achse

]]> <question><wirisCasSession><![CDATA[<session lang="de" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>plot</mi><mfenced><mi>f</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plotter1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><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="casSession"/></localData></question> Symmetrie 2 Welche der folgenden Funktionen ist achsensymmetrisch zur y-Achse?

]]> 1.0000000 0.3333333 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»5«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»5«/mn»«/msup»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»10«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»10«/mn»«/msup»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«msup»«mo»)«/mo»«mn»4«/mn»«/msup»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»-«/mo»«msup»«mi»x«/mi»«mn»10«/mn»«/msup»«mo»+«/mo»«mn»4«/mn»«msup»«mi»x«/mi»«mn»6«/mn»«/msup»«mo»+«/mo»«mn»2«/mn»«mi»x«/mi»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»-«/mo»«msup»«mi»x«/mi»«mn»8«/mn»«/msup»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»6«/mn»«/msup»«/math»

]]> <question><correctAnswers><correctAnswer></correctAnswer></correctAnswers></question> Der Graph einer Funktion f ist achsensymmetrisch zur y-Achse, wenn gilt:     f(-x)=f(x).

]]> Symmetrie 3 Bestimme die Variable c so, dass der Graph der Funktion «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mi»c«/mi»«/math» punkt- (zum Ursprung) bzw. achsensymmetrisch (zur y-Achse) ist.

]]> 1.0000000 0.3333333 0 true true none Die Funktion f(x) ist für jeden Wert von c punktsymmetrisch zum Ursprung

]]> Die Funktion f(x) ist für keinen Wert von c achsensymmetrisch zur y-Achse

]]> Die Funktion f(x) ist für c=0 achsensymmetrisch zur y-Achse

]]> Die Funktion f(x) ist für c=0 punktsymmetrisch zum Ursprung

]]> f(x) ist für jeden Wert von c achsensymmetrisch zur y-Achse

]]> Symmetrie 4 Erkenne die Symmetrie am Graphen der Funktion.

#d

]]> 1.0000000 0.3333333 0 true true abc f ist punktsymmetrisch zum Ursprung

]]> f ist punktsymmetrisch zur y-Achse

]]> f ist achsensymmetrisch zum Ursprung

]]> f ist weder symmetrisch zum Ursprung noch zur y-Achse.

]]> f ist achsensymmetrisch zur y-Achse

]]> <question><wirisCasSession><![CDATA[<session lang="de" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>plot</mi><mfenced><mi>f</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plotter1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><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="casSession"/></localData></question> Symmetrie 5 Der Graph einer Funktion f ist achsensymmetrisch zur y-Achse, wenn gilt…

]]> 1.0000000 0.3333333 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mrow»«mo»-«/mo»«mi»x«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mo»-«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«mi»f«/mi»«mo»(«/mo»«mo»-«/mo»«mi»x«/mi»«mo»)«/mo»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mo»-«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»-«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mo»-«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»-«/mo»«mi»f«/mi»«mo»(«/mo»«mo»-«/mo»«mi»x«/mi»«mo»)«/mo»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mo»-«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»f«/mi»«mo»(«/mo»«mo»-«/mo»«mi»x«/mi»«mo»)«/mo»«/math»

]]> <question><correctAnswers><correctAnswer></correctAnswer></correctAnswers></question> Symmetrie 6 Erkenne die Symmetrie am Graphen der Funktion.

#d

]]> 1.0000000 0.3333333 0 true true abc f ist punktsymmetrisch zum Ursprung

]]> f ist punktsymmetrisch zur y-Achse

]]> f ist achsensymmetrisch zum Ursprung

]]> f ist weder symmetrisch zum Ursprung noch zur y-Achse.

]]> f ist achsensymmetrisch zur y-Achse

]]> <question><wirisCasSession><![CDATA[<session lang="de" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>2</mn><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>plot</mi><mfenced><mi>f</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plotter1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><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="casSession"/></localData></question> Symmetrie 7 Welche der folgenden Funktionen ist achsensymmetrisch zur y-Achse?

]]> 1.0000000 0.3333333 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»4«/mn»«/msup»«mo»-«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»8«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»6«/mn»«/msup»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»4«/mn»«/msup»«mo»-«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»1«/mn»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»5«/mn»«/msup»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»+«/mo»«mn»1«/mn»«/math»

]]> Symmetrie 8 Welche der folgenden Funktionen ist punktsymmetrisch zum Koordinatenursprung ?

]]> 1.0000000 0.3333333 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»4«/mn»«/msup»«mo»-«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»8«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»6«/mn»«/msup»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»4«/mn»«/msup»«mo»-«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»1«/mn»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»5«/mn»«/msup»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»+«/mo»«mi»x«/mi»«/math»

]]> Symmetrie 9 Erkenne die Symmetrie am Graphen der Funktion.

#d

]]> 1.0000000 0.3333333 0 true true abc f ist punktsymmetrisch zum Ursprung

]]> f ist punktsymmetrisch zur y-Achse

]]> f ist achsensymmetrisch zum Ursprung

]]> f ist weder symmetrisch zum Ursprung noch zur y-Achse.

]]> f ist achsensymmetrisch zur y-Achse

]]> <question><wirisCasSession><![CDATA[<session lang="de" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="de">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>plot</mi><mfenced><mi>f</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plotter1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><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="casSession"></data></localData></question>