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prove that at least one of three trinomials has a real root

Source: 239MO 2004, grade 8-9, problem 1, proposed by S. Berlov

December 11, 2004
functionalgebra solvedalgebra

Problem Statement

Given non-constant linear functions p(x),q(x),r(x)p(x), q(x), r(x). Prove that at least one of three trinomials pq+r,pr+q,qr+ppq+r, pr+q, qr+p has a real root. proposed by S. Berlov
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