### JEE Main On 8 April 2017 Question 24

##### Question: Let p (x) be a quadratic polynomial such that p(0)=1. If p(x) leaves remainder 4 when divided by x-1 and it leaves remainder 6 when divided by x + 1, then: [JEE Online 08-04-2017]

#### Options:

A) $ p(-2)=19 $

B) $ p(2)=19 $

C) $ p(-2)=11 $

D) $ p(2)=11 $

## Show Answer

#### Answer:

Correct Answer: A

#### Solution:

- $ p(x)=ax^{2}+bx+c $ $ p(0)=1=c=1 $ $ . \begin{aligned} & p(1)=4 \\ & p(-1)=6 \\ \end{aligned} ] $ $ . \begin{aligned} & a+b+c=4 \\ & a-b+c=6 \\ \end{aligned} ]=. \begin{aligned} & a=4 \\ & b=-1 \\ \end{aligned} ] $ $ p(x)=4x^{2}-x+1 $ $ p(-2)=16+2+1=19 $