# Equation with polynomials

• Jun 22nd 2011, 07:51 AM
BakyX
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.
• Jun 22nd 2011, 11:20 AM
topsquark
Re: Equation with polynomials
Quote:

Originally Posted by BakyX
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 $\displaystyle F^2(x) = F(F(x))$ or $\displaystyle F^2(x) = (F(x))^2$ ?

-Dan
• Jun 23rd 2011, 12:57 AM
BakyX
Re: 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 AM
topsquark
Re: Equation with polynomials
Quote:

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

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