Let $α, β$ be the roots of $x^{2} + 3 x + 5 = 0$ then the equation whose roots are $- \frac{1}{α}$ and $- \frac{1}{β}$ is :

5 x^{2} - 3 x + 1 = 0

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5 x^{2} + 3 x - 4 = 0

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5 x^{2} - 3 x + 4 = 0

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5 x^{2} + 3 x - 1 = 0

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Solution

The correct option is A $5 x^{2} - 3 x + 1 = 0$
$α + β = - 3, α β = 5$

Required equation is $x^{2} - (\frac{- 1}{α} + \frac{- 1}{β}) x + (\frac{- 1}{α}) (\frac{- 1}{β}) = 0$
$\Rightarrow x^{2} + (\frac{α + β}{α β}) x + \frac{1}{α β} = 0$
$\Rightarrow x^{2} - \frac{3}{5} x + \frac{1}{5} = 0$
$\Rightarrow 5 x^{2} - 3 x + 1 = 0$

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