If \( \alpha \) and \( \beta \) are roots of \( a x^{2}+b x+c=0 \), the value of \( \lim _{x \ri...

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If \( \alpha \) and \( \beta \) are roots of \( a x^{2}+b x+c=0 \), the value of \( \lim _{x \rightarrow \alpha}\left(1+a x^{2}+b x+c\right)^{2 / x-\alpha} \) is
(a) \( e^{2 \alpha(\alpha-\beta)} \)
(b) \( \theta^{\alpha(\alpha-\beta)} \)
(c) \( \theta^{\frac{2 a}{3}(\alpha-\beta)} \)
(d) None of these
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