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Math Help - Solution to the cubic equation

  1. #1
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    Solution to the cubic equation

    Let a,b be positive real numbers. Prove there there exists a unique solution to x3+ax=b.

    I can prove that if there is a solution it is unique, but I'm not sure how to prove that a solution definitely exists.

    Any help would be great.

    Thanks!
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  2. #2
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    Re: Solution to the cubic equation

    All polynomials with real coefficients have as many complex roots as the degree of the polynomial. All nonreal roots appear as complex conjugates, so if the polynomial is of odd degree, there has to be at least one real root as it can't have a conjugate pair.
    Thanks from MarkFL and topsquark
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