smc

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 the pair (a,b) is

Accepted Answer

Since (x-a)(x-b) = x^2 - (a+b)x + ab = x^2 + ax + b = 0, it follows by comparing coefficients that -a - b = a and that ab = b. Since b is nonzero, a = 1, and -1 - b = 1 b = -2. Thus (a,b) = (1,-2).