NIMCET 2019 Question Paper with solutions

Question : 35 of 120

Marks: +1, -0

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

p(-2) = 11
p(2) = 11
p(2) = 10
p(-2) = 10
None of the above

Validate

Solution:

Given

p(x)=ax^2+bx+c

p(0)=c=1

⇒a+b=3

......(i)

p(-1)=a-b+1=6

⇒a-b=5

...(ii)
On solving Eqs. (i) and (ii), we get

a=4,b=1

∴\;\;p(x)=4x^2-x+1

p(-2)=16+2+1=19

p(2)=16-2+1=15

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