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Quadratic with f(f(sqrt2))=0

Source: St. Petersburg Math Olympiad, 2015, round II, grade 9, P1

September 30, 2016
quadraticsalgebrapolynomial

Problem Statement

Is there a quadratic trinomial f(x)f(x) with integer coefficients such that f(f(2))=0f(f(\sqrt{2}))=0 ?
A. Khrabrov
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