If \( \alpha, \beta \) are the distinct roots of \( x^{2}+b x+c=0 \), then \( \lim _{x \rightarrow \beta} \frac{e^{2\lef…

If \( \alpha, \beta \) are the distinct roots of \( x^{2}+b x+c=0 \), then

\( \lim _{x \rightarrow \beta} \frac{e^{2\left(x^{2}+b x+c\right)}-1-2\left(x^{2}+b x+c\right)}{(x-\beta)^{2}} \) is equal to

[JEE Main 2021, 27 Aug (Shift 1)]