anonymous
  • anonymous
What is the general form of a polynomial p(x) such that that\[ p(x^2)=p(x)^2\]
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
x^n
anonymous
  • anonymous
Darn, I went to take a drink of OJ and Avinash wrote it first.
anonymous
  • anonymous
\[f(x)=x\]

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anonymous
  • anonymous
lol ok i l make up for that
anonymous
  • anonymous
You're too nice, Avinash! :)
anonymous
  • anonymous
thanks i guess :)
anonymous
  • anonymous
or rather \[\left( f(x)\right) ^n=x^n\]
anonymous
  • anonymous
x^n
anonymous
  • anonymous
@eliassaab how do we can prove that only root of polynomial is 0?
anonymous
  • 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...
anonymous
  • 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
anonymous
  • anonymous
@eliassaab thank u sir for the nice problems u put up

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