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MathNet 2009-part-03 — 175 problems (EN–VI) Question 147

Math Olympiad Vault · MathNet 2009-part-03 — 175 problems (EN–VI)

Question 147

A quadratic trinomial $f(x)$ is chosen so that the equation
$$(f(x))^3 - f(x) = 0$$
has exactly $3$ real roots. Find the $y$-coordinate of the vertex of the graph of $f(x)$.