Question

Find the value of k for which roots of the equation x square + 5kx + 16 = 0 are real and equal ​

Answer 1

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Step-by-step explanation:

${x}^{2} + 5kx + 16 = 0 \\ \\ {b }^{2} - 4ac \\ \\ b = 5k \\ a = 1 \\ c = 16 \\ \\ {{5k}}^{2} - 4 \times 1 \times 16 \\ \\ 25 {k}^{2} - 84 = 0 \\ 25 {k}^{2} = 84 \\ {k}^{2} = \frac{84}{25 } \\ k = \sqrt{ \frac{84}{25} } \\ k = \frac{2 \sqrt{21} }{5}$

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