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Quadratic trinomials and linear function

Source: Tuymaada 2014, Day 2, Problem 1, Junior League

July 12, 2014
quadraticsfunctionalgebra solvedalgebraTuymaada

Problem Statement

For two quadratic trinomials P(x)P(x) and Q(x)Q(x) there is a linear function ℓ(x)\ell(x) such that P(x)=Q(ℓ(x))P(x)=Q(\ell(x)) for all real xx. How many such linear functions ℓ(x)\ell(x) can exist?
(A. Golovanov)
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