If the sum of the roots of the equation $k x^{2} + 2 x + 3 x = 0$ is equal to their product, then the value of k is
(a) $\frac{1}{3}$
(b) $\frac{- 1}{3}$
(c) $\frac{2}{3}$
(d) $\frac{- 2}{3}$

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Solution

(d) $\frac{- 2}{3}$
$Given: k x^{2} + 2 x + 3 k = 0 Sum of the roots = Product of the roots ⇒ \frac{- 2}{k} = \frac{3 k}{k} ⇒ 3 k = - 2 ⇒ k = \frac{- 2}{3}$

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