Question

Polynomials
find all polynomials P(x) with real coefficients such that:
\[P(2 P(x))=2 P(P(x))+2 (P(x))^2\]

Answer 1

I get:\[P(x)=x^2\]

Answer 2

yes thats one of the answers

Answer 3

Oh - I worked it out as the ONLY answer?

Answer 4

P(x) must be a poly of degree 2 at most - correct?

Answer 5

thats right

Answer 6

ok - maybe I made a mistake somewhere in my algebra - I'll try again...

Answer 7

ok

Answer 8

BTW: I'm assuming this is a challenge question and not something you need help in? :)

Answer 9

ok - gr8 - I do like the questions you put up - they make you think! :)

Answer 10

ok, I did make a mistake, so I now get 3 solutions:\[P(x)=x^2+bx\qquad\text{ for some constant }b\]\[P(x)=-\frac{1}{2}\]\[P(x)=0\]

Answer 11

@asnaseer
completely right

Answer 12

thanks for letting me know! :)

Answer 13

yw ;)