If \( \lim _{x \rightarrow 0}\left(1+a x+b x^{2}\right)^{2 / x}=e^{3} \), the values of \( a \) ...

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If \( \lim _{x \rightarrow 0}\left(1+a x+b x^{2}\right)^{2 / x}=e^{3} \), the values of \( a \) and \( b \) are
(a) \( a=\frac{3}{2}, b \in R \)
(b) \( a=\frac{1}{2}, b \in R \)
(c) \( a \in R, b \in R \)
(d) None of these
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