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Question

The value of n for which the expression 9x4−12x3+nx2−8x+4 becomes a perfect square is

A
12
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B
16
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C
18
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D
24
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Solution

The correct option is B 16
Let the equation be of the form (ax2+bx+c)2=a2x4+b2x2+c2+2abx3+2bxc+2acx2
a2x4+2abx3+(b2+2ac)x2+c2+2bxc = 9x412x3+nx28x+4
Comparing the coefficients, a=3,c=2
2ab=12
b=2
Therefore, n=b2+2ac =4+12=16

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