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f(c)f(-c)>=f(a) where f(x)=x^2-2ax+b

Source: 2022 Turkey JBMO TST P6

March 15, 2022
Inequalityreal number

Problem Statement

Let cc be a real number. If the inequality f(c)⋅f(−c)≥f(a)f(c)\cdot f(-c)\ge f(a) holds for all f(x)=x2−2ax+bf(x)=x^2-2ax+b where aa and bb are arbitrary real numbers, find all possible values of cc.
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