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Let p(x)=ax2+bx+c,q(x)=lx2+mx+n. If p(1)q(1)=0, p(2)q(2)=1 and p(3)q(3)=4, then p(4)q(4) equals

A
0
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B
5
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C
6
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D
9
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Solution

The correct option is D 9
Let p(x)=ax2+bx+c and q(x)=lx2+mx+n.
Now p(x)q(x)=(al)x2+(bm)x+(cn)=Ax2+Bx+C(let).

Given
p(1)q(1)=0
A+B+C=0......(1).

Also given
p(2)q(2)=1
or, 4A+2B+C=1........(2).

Again
p(3)q(3)=4
or, 9A+3B+C=4..........(3).

Solving from (1),(2) and (3) we get,
A=1,B=2,C=1.

Now p(4)q(4)
=16A+4B+C=16(1)+4(2)+1=9

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