Consider \( P(x)=a x^{2}+b x+c \), where \( a, b, c \in R \) and \(... VIDEO
Consider \( P(x)=a x^{2}+b x+c \), where \( a, b, c \in R \) and \( P(2)=9 \). Let \( \alpha \) and \( \beta \) be the roots of the equation \( P(x)=0 \).
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If \( \alpha \rightarrow \infty \) and \( P^{\prime}(3)=5 \) then \( \lim _{x \rightarrow \infty}\left(\frac{P(x)}{5(x-1)}\right)^{x} \) is equal to :
(a) 1
(b) \( e^{\frac{1}{5}} \)
(c) \( e^{\frac{4}{5}} \)
(d) \( e^{\frac{2}{5}} \)
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