AMC 12 2002b Problem 6

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

$\mathrm{(A)}\ (-2,1) \mathrm{(B)}\ (-1,2) \mathrm{(C)}\ (1,-2) \mathrm{(D)}\ (2,-1) \mathrm{(E)}\ (4,4)$