MathDB
Nice roots problem [Iran Second Round 1990]

Source:

December 1, 2010
algebrapolynomialquadraticsquadratic formulaalgebra proposed

Problem Statement

Let α\alpha be a root of the equation x3−5x+3=0x^3-5x+3=0 and let f(x)f(x) be a polynomial with rational coefficients. Prove that if f(α)f(\alpha) be the root of equation above, then f(f(α))f(f(\alpha)) is a root, too.
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