Question

If one root of 5x2 + 13x + k = 0 is the reciprocal of the other root, then find value of k. Or if arithmetic mean of two numbers a and b is 8 and ab = 9, find a quadratic equation whos

Answer 1

Hey

$5x {}^{2} + 13x + k = 0 \\ let \alpha \: be \: one \: zero \\ other \: zero \: would \: be \: \frac{1}{ \alpha } \\ \\ product \: of \: zeros = \frac{k}{15 } \\ = > \alpha \times \frac{1}{ \alpha } = \frac{k}{15 } \\ = > \frac{k}{15} = 1 \\ = > k = 15$


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