MathDB

3

Part of 2016 Latvia Baltic Way TST

Problems(1)

roots of P (Q(x)) are -2015, ..., 2017 if P has degree 2016, Q is trinomial

Source: 2016 Latvia BW TST P3

12/17/2022
Given a polynomial PP of degree 20162016 with real coefficients and a quadratic polynomial QQ with real coefficients. Is it possible that the roots of the polynomial P(Q(x))P (Q(x)) are exactly all these numbers: −2015,−2014,...,−2,−1,1,2,...,2016,2017?-2015, -2014, . . . , -2, -1, 1, 2, . . . , 2016, 2017?
algebrapolynomial