# Difference between revisions of "004 Sample Final A, Problem 8"

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− | :: <span class="exam"> a) List all the possible rational zeros of the function <math>f(x)=x^4-4x^3-7x^2+34x-24.</math> <br> | + | :: <span class="exam"> a) List all the possible rational zeros of the function <math>f(x)=x^4-4x^3-7x^2+34x-24.</math> </span><br> |

− | :: b) Find all the zeros, that is, solve <math>f(x) = 0</math> | + | :: <span class="exam"> b) Find all the zeros, that is, solve <math>f(x) = 0</math> |

{| class="mw-collapsible mw-collapsed" style = "text-align:left;" | {| class="mw-collapsible mw-collapsed" style = "text-align:left;" | ||

! Foundations | ! Foundations |

## Latest revision as of 10:18, 2 June 2015

- a) List all the possible rational zeros of the function
- b) Find all the zeros, that is, solve

- a) List all the possible rational zeros of the function

Foundations |
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If , what does the rational roots tell us are the possible roots of ? |

Answer: |

The rational roots tells us that the possible roots of are where is a divisor of . |

Solution:

Step 1: |
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By the rational roots test, the possible roots of are . |

Step 2: |
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Using synthetic division, we test 1 as a root of . We get a remainder of 0. So, we have that 1 is a root of . |

By synthetic division, . |

Step 3: |
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Using synthetic division on , we test 2 as a root of this function. We get a remainder of 0. So, we have that 2 is a root of . |

By synthetic division, . |

Step 4: |
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Thus, . |

The zeros of are . |

Final Answer: |
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The possible roots of are . |

The zeros of are |