# let $\alpha$ and $\beta$ be the distinct roots of $ax^2+bx+c=0$ then $\lim\limits_{x\to \alpha}\large\frac{1-\cos(ax^2+bx+c)}{(x-\alpha)^2}$ is equal to
$\begin{array}{1 1}(a)\;-\large\frac{a^2}{2}\normalsize (\alpha-\beta)^2&(b)\;\large\frac{1}{2}\normalsize(\alpha-\beta)^2\\(c)\;\large\frac{a^2}{2}\normalsize(\alpha-\beta)^2&(d)\;0\end{array}$