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f(x)) ^3- f(x)$ has exactly three real roots, , trinomial

Source: All-Russian MO 2009 Regional 10. 1

August 27, 2024
algebrapolynomial

Problem Statement

Square trinomial f(x)f(x) is such that the polynomial (f(x))3āˆ’f(x)(f(x)) ^3- f(x) has exactly three real roots. Find the ordinate of the vertex of the graph of this trinomial.
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