jmc

Question

Suppose that a and b are nonzero real numbers, and that the equation x^2 + ax + b = 0 has solutions a and b. Then what is the pair (a,b)?

Accepted Answer

The given conditions imply that x^2 + ax + b = (x-a)(x-b) = x^2 -(a+b)x + ab, so a+b = -a and ab = b. Since b 0, the second equation implies that a=1. The first equation gives b=-2, so (a,b) = (1,-2).