Question

Find the value of $k$ so that the sum of the roots of the quadratic equation ${kx}^2+2x+3k=0$ is equal to their product.

• A. $\frac{2}{3}$
• B. $\frac{-2}{3}$
• C. $\frac{3}{2}$
• D. $\frac{-3}{2}$

Answer 1

The correct option is B $\frac{-2}{3}$

Given equation is: ${kx}^2+2x+3k=0$
Comparing with $a{x}^2+bx+c=0$

$\Rightarrow a=k,b=2,c=3k.$
Sum of roots $=\frac{-b}{a}=\frac{-2}{k}$
Product of the roots $=\frac{c}{a}=\frac{3k}{k}$
Since sum of roots = Product of roots
$\Rightarrow \frac{-2}{k}=\frac{3k}{k}$

$\Rightarrow \frac{-2}{k}=\frac{3}{1}$
$\Rightarrow 3k=-2$

$\Rightarrow k=\frac{-2}{3}$