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Math Help - Roots of a sum of polynomials

  1. #1
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    Roots of a sum of polynomials

    Hello, here is the question I am working on:

    If u and v are two roots of the polynomial

    {x}^{4}+{x}^{3}-1

    then show u *v is a root of

    {x}^{6}+{x}^{4}+{x}^{3}-{x}^{2}-1

    Now I know that this is true, and the brute force is to consider that the product of the roots of the first polynomial is -1, then match up the expansion of the second polynomial. I was wondering if there is a special relation between the roots of a sum of polynomials to the roots of the originals, since the second polynomial is the sum of the first one and

    {x}^{6}-{x}^{2}

    which has simple roots -1,1,0,0,-i,i

    Does anyone know a shortcut proof for this?
    Thanks.
    Last edited by spammanon; March 24th 2008 at 03:50 PM. Reason: Fix an error
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