Let $\alpha$ and $\beta$ be the distinct roots of $ax^2 + bx + c = 0 $, then $\displaystyle{\lim_{x \to \alpha} \frac{1- \cos (ax^2 + bx + c)}{(x-\alpha)^2}}$ is equal to :

Question

( A ) $\frac{1}{2} (\alpha - \beta)^2$
( B ) $-\frac{a^2}{2} (\alpha - \beta)^2$
( C ) $\frac{a^2}{2} (\alpha - \beta)^2$
( D ) 0