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

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Solution

The given quadratic equation is 9x² + 8kx + 16 = 0
The equation has equal root if its discriminant is zero.
D=b² -4ac

(8k)² -4(9)(16)

64k² -576

64k² = 576

k² = 576/64

k = 24/8

k = 3

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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.

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