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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- Jun 22nd 2011, 07:51 AMBakyXEquation 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. - Jun 22nd 2011, 11:20 AMtopsquarkRe: Equation with polynomials
- Jun 23rd 2011, 12:57 AMBakyXRe: Equation with polynomials
My work..I really don't now, how to start. Sorrry. F^2(x)=(F(x))^2

- Jun 23rd 2011, 08:53 AMtopsquarkRe: Equation with polynomials
F(y) = \sum_n a^n y^n[/tex]

So

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

We also have

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

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

-Dan