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Question

For non-zero distinct real numbers a1 and a2, let f(x)=a1x2+b1x+c1,g(x)=a2x2+b2x+c2 and p(x)=f(x)g(x). If p(x)=0 only at x=1 and p(2)=2, then the value of p(2) is 


A
9
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B
6
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C
18
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D
3
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Solution

The correct option is C 18
p(x)=f(x)g(x)=(a1a2)x2+(b1b2)x+(c1c2)
Let p(x)=ax2+bx+c where a=a1a20
It is given that p(x)=0 only for x=1.
Therefore, p(x)=0 has equal roots, both roots are x=1
So,
p(x)=a(x+1)2(1)
Now, we know that
p(2)=2
Putting x=2 in equation (1),
a=2
p(x)=2(x+1)2

Hence, the value of
p(2)=18.

Mathematics

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