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given non-constant linear functions

Source: 239MO 2004, grade 10-11, problem 1

December 11, 2004

functionalgebrapolynomialalgebra solvedPolynomials

Problem Statement

Given non-constant linear functions

p_1(x), p_2(x), \dots p_n(x)

. Prove that at least

n-2

of polynomials

p_1p_2\dots p_{n-1}+p_n, p_1p_2\dots p_{n-2} p_n + p_{n-1},\dots p_2p_3\dots p_n+p_1

have a real root.