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Construct T using three polynomials P, Q, R with given roots

Source: IMO LongList 1970 - P52

May 22, 2011
algebrapolynomialalgebra proposed

Problem Statement

Let P,Q,RP,Q,R be polynomials and let S(x)=P(x3)+xQ(x3)+x2R(x3)S(x) = P(x^3) + xQ(x^3) + x^2R(x^3) be a polynomial of degree nn whose roots x1,…,xnx_1,\ldots, x_n are distinct. Construct with the aid of the polynomials P,Q,RP,Q,R a polynomial TT of degree nn that has the roots x13,x23,…,xn3.x_1^3 , x_2^3 , \ldots, x_n^3.
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