$y x^{2} - 12 x + k$ is a perfect square find the numerical nature of $k$

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Solution

Considering the equation to be: $4 x^{2} - 12 x + k$

$(a - b)^{2} = a^{2} - 2 a b + b^{2}$

$4 x^{2} - 12 x + k = a^{2} - 2 a b + b^{2}$

$a = 2 x$

$- 2 a b = - 12 x$

$\Rightarrow a b = 6 x$

$\Rightarrow (2 x) b = 6 x \Rightarrow b = 3$

$∴ k = 3$

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