For the equation $ 3x^2 + 8x + 2 = 0 $, if the roots are $ \alpha $ and $ \beta $, then what is the value of $ \frac{1}{\alpha} + \frac{1}{\beta} $?"

Q.For the equation $ 3x^2 + 8x + 2 = 0 $, if the roots are $ \alpha $ and $ \beta $, then what is the value of $ \frac{1}{\alpha} + \frac{1}{\beta} $?" (a) -$\cfrac{3}{8}$ (b) $\cfrac{2}{3}$ (c) -4 (d) 4

Answer: C

As $ 3x^2 + 8x + 2 = 0 $
Therefore, $\alpha + \beta = -\cfrac{8}{3}$ and $\alpha\beta=\cfrac{2}{3}$

$\therefore \cfrac{1}{\alpha}+\cfrac{1}{\beta}$
= $\cfrac{\beta+\alpha}{\alpha\beta}$
=$\cfrac{-\cfrac{8}{3}}{\cfrac{2}{3}}$
=$-\cfrac{8}{3}\times \cfrac{3}{2}=-4$

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