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Let $α$ and $β$ be the roots of the equation $3 x^{2} - 6 x + 5 = 0$ then the equation whose roots are $(α + β) a n d \frac{2}{(α + β)}$ is

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

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

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

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

answer is C.

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Detailed Solution

$\begin{array}{l} α + β = 2 a n d α β = \frac{5}{3} \\ x^{2} - x [(α + β) + \frac{2}{α + β}] + 2 = 0 \\ x^{2} - x [3] + 2 = 0 \end{array}$

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