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

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Solution

For the polynomial $4 x^{2} - k x + 9$ to be a perfect square
Discriminant should be zero
$⟹ k^{2} - (4) (4) (9) = 0$
$⟹ k = \pm 12$

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