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Vietnam NMO 1990_5

Source:

October 26, 2008
algebrapolynomialfunctional equationalgebra unsolved

Problem Statement

Suppose f(x)\equal{}a_0x^n\plus{}a_1x^{n\minus{}1}\plus{}\ldots\plus{}a_{n\minus{}1}x\plus{}a_n (a0≠0 a_0\neq 0) is a polynomial with real coefficients satisfying f(x)f(2x^2) \equal{} f(2x^3 \plus{} x) for all x∈R x \in\mathbb{R}. Prove that f(x) f(x) has no real roots.
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