BITSAT-2015 Problem

Calculus Level 4

If \(P(x)\) is a quadratic polynomial satisfying

\(P(0) = 6\), \(P(1) = 2\), \(P(2) = 0\).

And \(\displaystyle f(x) = \sum_{ n = 0}^{\infty } \dfrac{P(n)}{n!.2^n} x^n\)

Then \(f(x)\) is

Note:- I have changed the options from the original ones.
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