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 Ap(−2)=19 p(x)=ax2+bx+c
p(0)=1=c=1
p(1)=4p(−1)=6]
a+b+c=4a−b+c=6] subtracting the above equations, we get 2b=−2⇒b=−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,