The value of n for which the expression $9 x^{4} - 12 x^{2} + n x^{2} - 8 x + 4$ becomes a perfect square, is

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Solution

The correct option is B 16
Given, $9 x^{4} - 12 x^{2} + n x^{2} - 8 x + 4$
$if this is a perfect square it is perfect square for any x$ .
$put x=1 in given polynomial$ .
$\Rightarrow 9 - 12 + n - 8 + 4 is a perfect square$ .
$\Rightarrow n - 7 is a perfect square$
Here, $n - 7 is a perfect square only n=16$
$∵ 16 - 7 = 9$
$9 is a perfect square$
Option B is correct.

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