Find the values of $k$ for which the given equation has real and equal roots
$9 x^{2} + 3 k x + 4 = 0$

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Solution

The given equation is $9 x^{2} + 3 k x + 4 = 0$

Here, $∴ D = b^{2} - 4 a c = {(3 k)}^{2} - 4 \times 9 \times 4 = 9 k^{2} - 144$

The equation will have real and equal roots, if

$D = 0 \Rightarrow 9 k^{2} - 144 = 0 \Rightarrow k^{2} = \frac{144}{9} \Rightarrow k^{2} = 16 \Rightarrow k = \pm 4$

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Similar questions

{9 x}^{2} + 3 k x + 4 = 0

Find the nonzero value of k for which the roots of the quadratic equation $9 x^{2} - 3 k x + k = 0$ are real and equal.

9 x^{2} - 3 k x + k = 0

9 x^{2} + 3 k x + 4 = 0

k

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