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Math Help - Equation with polynomials

  1. #1
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    Equation with polynomials

    Hello. I have big problem with this quest:

    Find all polynomials F(x), that answers equation

    F(x^2-2x) = F^2 (x-2)

    Be detail, please and sorry for ENG.
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Equation with polynomials

    Quote Originally Posted by BakyX View Post
    Hello. I have big problem with this quest:

    Find all polynomials F(x), that answers equation

    F(x^2-2x) = F^2 (x-2)

    Be detail, please and sorry for ENG.
    First of all, please show us any work that you have done on this.

    Second: Is F^2(x) = F(F(x)) or F^2(x) = (F(x))^2 ?

    -Dan
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  3. #3
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    Re: Equation with polynomials

    My work..I really don't now, how to start. Sorrry. F^2(x)=(F(x))^2
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  4. #4
    Forum Admin topsquark's Avatar
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    Re: Equation with polynomials

    Quote Originally Posted by BakyX View Post
    Hello. I have big problem with this quest:

    Find all polynomials F(x), that answers equation

    F(x^2-2x) = F^2 (x-2)

    Be detail, please and sorry for ENG.
    F(y) = \sum_n a^n y^n[/tex]

    So
    F(x^2 - 2x) = \sum_n a_n(x^2 - 2x)^n = a_0 + a_1(x^2 - 2x) + ~...

    We also have
    \left [ F(x^2 - 2x \right ] ^2 = \sum_m \sum _n a_m a_n (x^2 - 2x)^{m + n}

    Work out some terms for the F squared series and compare them.

    -Dan
    Last edited by topsquark; June 23rd 2011 at 08:55 AM. Reason: Fixed the typos
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