For what values of $k$ , the roots of $9 x^{2} + 8 k x + 16 = 0$ are real and equal.

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Solution

Given equation is $9 x^{2} + 8 k x + 16 = 0$
For real and equal roots
$D = 0$
i.e., $b^{2} - 4 a c = 0 {(8 k)}^{2} - 4 \times 9 \times 16 = 0 \Rightarrow 64 k^{2} - 36 \times 16 = 0 \Rightarrow 64 k^{2} - 576 = 0 \Rightarrow 64 k^{2} = 576 \Rightarrow k^{2} = \frac{576}{64} = 9 \Rightarrow k = \pm 3$
values of $k - 3, 3$

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