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Cyclic permutation of roots

Source: Centroamerican Olympiad 2016, problem 3

June 19, 2016

algebrapolynomialroots

Problem Statement

The polynomial

Q(x)=x^3-21x+35

has three different real roots. Find real numbers

a

and

b

such that the polynomial

x^2+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

.

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