If the roots of the equation $5 x^{2} - 7 x + k = 0$ are mutually reciprocal then $k =$

5

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2

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\frac{1}{5}

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None of these

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Solution

The correct option is A $5$
$5 x^{2} - 7 x + k = 0$
Let $α & \frac{1}{α}$ are the roots of the given equation ,then
$α \times \frac{1}{α} = \frac{k}{5} (p r o d u c t o f t h e z e r o e s = \frac{c}{a})$
$\Rightarrow 1 = \frac{k}{5}$
$\Rightarrow k = 5$

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