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(a-b)^2 Expansion and Visualisation

For what valu...

Question

For what value of ' $k$ ' the polynomial ${4 x}^{2} - k x + 9$ is a perfect square.

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Solution

$= {4 x}^{2} - k x + 9$
$= {(2 x)}^{2} - k x + {(3)}^{2}$
Comparing it with $a^{2} - 2 a b + b^{2}$
we get,
$k = 2 \times 2 \times 3 = 12$

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