anonymous 4 years ago What is the general form of a polynomial p(x) such that that$p(x^2)=p(x)^2$

1. anonymous

x^n

2. anonymous

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

3. anonymous

$f(x)=x$

4. anonymous

lol ok i l make up for that

5. anonymous

You're too nice, Avinash! :)

6. anonymous

thanks i guess :)

7. anonymous

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

8. anonymous

x^n

9. anonymous

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

10. anonymous

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...

11. anonymous

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

12. anonymous

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