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Quadratic Trinomial

Source: All Russia 2015 grade 9 Day 1 P1

December 12, 2015

quadraticsnumber theoryalgebra

Problem Statement

Real numbers

a

and

b

are chosen so that each of two quadratic trinomials

x^2+ax+b

and

x^2+bx+a

has two distinct real roots,and the product of these trinomials has exactly three distinct real roots.Determine all possible values of the sum of these three roots. (S.Berlov)

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