JEE Math Practice Question

Let $$\alpha$$ and $$\beta$$ be the distinct roots of $$a{x^2} + bx + c = 0$$, then $$\mathop {\lim }\limits_{x \to \alpha } {{1 - \cos \left( {a{x^2} + bx + c} \right)} \over {{{\left( {x - \alpha } \right)}^2}}}$$ is equal to

1. A.$${{{a^2}{{\left( {\alpha - \beta } \right)}^2}} \over 2}$$
2. B.0
3. C.$$ - {{{a^2}{{\left( {\alpha - \beta } \right)}^2}} \over 2}$$
4. D.$${{{{\left( {\alpha - \beta } \right)}^2}} \over 2}$$