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Math Help - Polynomial proof

  1. #1
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    Polynomial proof

    Polynomial proof-2014-08-05-19.51.45.jpg
    Can somebody just solve it? I've tryied , even used the mathematical induction, but it didnt work and i need to have this done. No it's not a homework. thanks for help.
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  2. #2
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    Re: Polynomial proof

    Try long division...? The first quotient being x^(n-2)*sin(a).
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  3. #3
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    Re: Polynomial proof

    For $n=1$ your conclusion is false unless $\sin(\alpha)=0$, in which case W(x) is identically 0 and the result is trivial. For $n>1$ if $\sin(\alpha)=0$ then W(x)=0 and then again the result is trivial. So I restated your problem:

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  4. #4
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    Re: Polynomial proof

    Here is my suggestion: use the quadratic formula to solve $Q(x)$ and then use DeMoivre's formula.
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