Let \( P(x) \) be a quadratic polynomial with real coefficients suc...

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Let \( P(x) \) be a quadratic polynomial with real coefficients such that \( 2(1+P(x))=P(x-1)+P(x+1) \) is true for all \( x \in R \). Given
\( \mathrm{P} \) \( P(0)=8 \) and \( P(2)=32 \).

W)
Sum of coefficients of \( P(x) \) is
(a) 20
(b) 19
(c) 17
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