Find all polynomials with real coefficients, for which the equality
P(2P(x))=2P(P(x))+2(P(x))2
holds for any real number x.
(In reply to
Thoughts by Brian Smith)
Ah, yes, I made a math error 3.5 years ago. Corrected:
If the highest order term of P(x) is bx^2, then
the Left hand side's highest order term is b(2bx^2)^2 = 4(b^3)x^4, and
the Right hand side's highest order term is 2b(bx^2)^2 + 2(bx^2)^2) = 2(b^3)x^4 + 2(b^2)x^4
So 4b^3 must equal 2b^3 + 2b^2.
So either b = 0 or b =1
Solutions are P(x) = 0 or P(x) = x^2
re: Thoughts
