MathDB

P(Q(x)) has only the zeros at x= 2,3,5,7 wher P,Q trinomials

Source: Dutch BxMO/EGMO TST 2012 p1

August 24, 2019

trinomialquadraticspolynomialrootsalgebra

Problem Statement

Do there exist quadratic polynomials

P(x)

and

Q(x)

with real coeffcients such that the polynomial

P(Q(x))

has precisely the zeros

x = 2, x = 3, x =5

and

x = 7