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Found problems: 1

2016 Saint Petersburg Mathematical Olympiad, 1
Tags: trinomial , quadratic trinomial , common real root , algebra
Given three quadratic trinomials $f, g, h$ without roots. Their elder coefficients are the same, and all their coefficients for x are different. Prove that there is a number $c$ such that the equations $f (x) + cg (x) = 0$ and $f (x) + ch (x) = 0$ have a common root.