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Let P(x) be quadratic polynomical with r...

Let `P(x)` be quadratic polynomical with real coefficient such tht for all real `x` the relation `2(1 + P(x)) = P(x - 1) + P(x + 1)` holds. If `P(0) = 8` and `P(2) = 32` then
Sum of all coefficients of `P(x)` can not be

A

`20`

B

`19`

C

`17`

D

`15`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Put `x = 1`
`2(l + P(1)) = P(0) + P(2) rArr P(1) = 19`
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  • Let P(x) be quadratic polynomical with real coefficient such tht for all real x(1) the relation 2(1 + P(x)) = P(x - 1) + P(x + 1) holds. If P(0) = 8 and P(2) = 32 then If the range of P(x) is [m, oo) then 'm' is less then (A) -12 (B) -15 (C) -17 (D) -5

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