Problem

Source: Centroamerican Olympiad 2016, problem 3

Tags: algebra, polynomial, roots



The polynomial Q(x)=x321x+35 has three different real roots. Find real numbers a and b such that the polynomial x2+ax+b cyclically permutes the roots of Q, that is, if r, s and t are the roots of Q (in some order) then P(r)=s, P(s)=t and P(t)=r.