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Let P(x) be a polynomial of degree 11 su...

Let `P(x)` be a polynomial of degree `11` such that `P(x) = (1)/(x + 1)` for `x = 0, 1, 2, 3,"…."11`. The value of `P(12)` is.

A

`(1)/(13)`

B

`1`

C

`0`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
`(x+1)P(x) - 1 = a(x) (x-1)(x-2)"…."(x-11)"……(1)`
Put `x = -1`
`0 - 1 = a(-1)(-2)"……"(-12)`
`a = (-1)/(12)`
from eq. `(1)` put `a = (-1)/(12), x = 12`
`13 P(12) -1 = (-1)/(12)(12)(11)"……"(1) = P (12) = 0`
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