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