Square trinomial $f(x)$ is such that the polynomial $(f(x)) ^3- f(x)$ has exactly three real roots. Find the ordinate of the vertex of the graph of this trinomial.
Source: All-Russian MO 2009 Regional 10. 1
Tags: algebra, polynomial
Square trinomial $f(x)$ is such that the polynomial $(f(x)) ^3- f(x)$ has exactly three real roots. Find the ordinate of the vertex of the graph of this trinomial.