Question

What is the general form of a polynomial p(x) such that that\[ p(x^2)=p(x)^2\]

Answer 1

x^n

Answer 2

Darn, I went to take a drink of OJ and Avinash wrote it first.

Answer 3

\[f(x)=x\]

Answer 4

lol ok i l make up for that

Answer 5

You're too nice, Avinash! :)

Answer 6

thanks i guess :)

Answer 7

or rather \[\left( f(x)\right) ^n=x^n\]

Answer 8

x^n

Answer 9

@eliassaab
how do we can prove that only root of polynomial is 0?

Answer 10

Apart from 0 complex numbers with |a| = 1 are only possible roots but i cant cancel them.
it seems easier than the other problems but i dony know...

Answer 11

i think its trivial because there r infinite complex numbers with |a| = 1 and if one of them is root then the others must be too and this is not true because a polynomial can only have a finite number of roots

Answer 12

@eliassaab
thank u sir
for the nice problems u put up