Limit related problems in differentiation Suppose $\alpha$ and $\beta$ are two roots of the equation $ax^2+bx+c=0$. Find
$$\lim_{x\to\alpha}\frac{1-\cos(ax^2+bx+c)}{(x-\alpha)^2}$$
Please help me to solve this calculus problem

HINT
We have
$$\frac{1-\cos(ax^2+bx+c)}{(x-\alpha)^2}=\frac{1-\cos[a(x-\alpha)(x-\beta)]}{a^2(x-\alpha)^2(x-\beta)^2}a^2(x-\beta)^2$$
then refer to standard limit as $t\to 0$
$$\frac{1-\cos t}{t^2}\to \frac12$$
