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Math Help - Roots of polynomial

  1. #1
    Member
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    Roots of polynomial

    How do i prove that the following has a root between 0 and 4?

    p(x)=x^5-4x^4-10x^2+40x

    Thanks
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  2. #2
    MHF Contributor
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    Talking

    Use what you learned back in algebra:

    What did you see when you graphed this polynomial?

    What signs did you get on the values of f(1), f(2), and f(3)?

    What did you conclude, on the basis of the Intermediate Value Theorem?

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  3. #3
    Junior Member
    Joined
    Nov 2009
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    For F(0)=0
    F(1)= 27
    F(2)= 8
    F(3)= -51
    F(4)=0

    And we know the graph is continuous since it is a polynomial.

    So how would one use the IVT to prove the roots are between F(0) and F(4).
    Should it not be between F(2) and F(3)

    Thanks
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