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

$x^{2} - 3 x - 10 = 0$

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$x^{2} + 3 x + 10 = 0$

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$x^{2} - 3 x + 10 = 0$

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$x^{2} + 3 x - 10 = 0$

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Solution

The correct option is D
$x^{2} + 3 x - 10 = 0$

$2 x^{2} - 3 x - 5 = 0$

$α + β = \frac{3}{2}, α β = \frac{- 5}{2}$

Let $λ_{1}, λ_{2}$ be the sum and product of the transformed equation.
$\Rightarrow λ_{1} = \frac{5}{α} + \frac{5}{β}$ $= 5 \times \frac{(α + β)}{α β} = - 3$

$& λ_{2} = \frac{25}{α β} = - 10$
Thus, transformed equation is:
$x^{2} + λ_{1} x + λ_{2} = 0$
$\Rightarrow x^{2} + 3 x - 10 = 0$

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