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(f(x))^5 - f(x) has exactly three real roots, trinomial

Source: All-Russian MO 2009 Regional 11. 1

August 28, 2024
algebrapolynomial

Problem Statement

Square trinomial f(x)f(x) is such that the polynomial (f(x))^5 - f(x) has exactly three real roots. Find the ordinate of the vertex of the graph of this trinomial.