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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 which one is correct?

A
p(2)=11
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B
p(2)=19
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C
p(2)=11
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D
p(2)=19
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Solution

The correct option is A p(2)=19
p(x)=ax2+bx+c

p(0)=1=c=1

p(1)=4p(1)=6]

a+b+c=4ab+c=6]
subtracting the above equations, we get 2b=2b=1
adding the above two equations and putting values of c, we get
2(a+c)=10
a+c=5
a+1=5
a=4

putting the values in the specified general equation,

p(x)=4x2x+1

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

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