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.

(In reply to

Solution by Brian Smith)

I am not clear on one point. Can't the larger root of one equal the larger root of the other? Can't the smaller root of one equal the smaller root of the other? Aren't there two other cases besides the case that was analyzed?