Find the value of k for which the roots of 9x^{2} + 8kx + 16 = 0 are real and equal.

Given that the quadratic equation 9x^{2} + 8kx + 16 = 0 roots are real and equal.

Comparing with standard quadratic equation ax^{2} + bx + c = 0

a = 9 b = 8k c = 16

Thus D = 0

Discriminant D = b^{2} – 4ac = 0

(8k)^{2} – 4.9.16 = 0

64k^{2} – 576 = 0

k^{2} = 9 taking square root both sides

Thus k = 3 or k = – 3 for which the roots are real and equal.

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