# 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

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