AMC 12 2003a Problem 25

Let $f(x)= \sqrt{ax^2+bx}$. For how many real values of $a$ is there at least one positive value of $b$ for which the domain of $f$ and the range of $f$ are the same set?

$\mathrm{(A) \ 0 } \mathrm{(B) \ 1 } \mathrm{(C) \ 2 } \mathrm{(D) \ 3 } \mathrm{(E) \ \mathrm{infinitely \ many} }$