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Math Help - Proving the root of a cubic polynomial

  1. #1
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    Proving the root of a cubic polynomial

    How, would I go about proving the root exists for:

    x^3+5x^2-4x-1 in the interval [0,1]

    I'm a little lost as to how I should start.

    Thanks.
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  2. #2
    A Plied Mathematician
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    Re: Proving the root of a cubic polynomial

    Try using the Intermediate Value Theorem. Does that give you any ideas?
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  3. #3
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    Re: Proving the root of a cubic polynomial

    It seems like I'm not doing anything though f(0) = -1 and f(1) = 1 and all you say is therefore by the intermediate value there must exist an x such that f(x) = 0 because f(0) is negative and f(1) is positive?

    Am I missing any steps in the proof? Just lean on the theorem and do nothing?
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  4. #4
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    Re: Proving the root of a cubic polynomial

    Quote Originally Posted by terrorsquid View Post
    It seems like I'm not doing anything though f(0) = -1 and f(1) = 1 and all you say is therefore by the intermediate value there must exist an x such that f(x) = 0 because f(0) is negative and f(1) is positive?

    Am I missing any steps in the proof? Just lean on the theorem and do nothing?
    If the function goes from negative to positive, or vice versa, then it must cross the x-axis somewhere in between. That's all you need to do
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  5. #5
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    Re: Proving the root of a cubic polynomial

    Quote Originally Posted by Prove It View Post
    If the function goes from negative to positive, or vice versa, then it must cross the x-axis somewhere in between. That's all you need to do
    Continuous function

    CB
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  6. #6
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    Re: Proving the root of a cubic polynomial

    Quote Originally Posted by CaptainBlack View Post
    Continuous function

    CB
    That is very true, and I should have pointed it out, but since polynomials are continuous and the function given by the OP is a polynomial, I thought it went without speaking. But thanks
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