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

If \(\alpha ,\beta\) are the distinct roots of \({x}^{2}+bx+c=0\), then \(\lim _{x\to \beta }\frac{{e}^{2\left({x}^{2}+bx+c\right)}-1-2\left({x}^{2}+bx+c\right)}{(x-\beta {)}^{2}}\) is equal to

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