Question

If the sum of the roots of the equation $\lambda x^2+2x+3\lambda =0$ be equal to their product $\&\lambda \ne 0,$ then find the value of $\lambda .$

• A. $-\frac{2}{3}$
• B. -4
• C. 6
• D. 4

Answer 1

The correct option is A

$-\frac{2}{3}$

Given quadratic equation
$\lambda x^2+2x+3\lambda =0$
Now, Sum of roots $=\frac{-2}{\lambda }$
And, product of roots $=\frac{3\lambda }{\lambda }=3$

According to condition that sum of roots is equal to the product of roots.
$\Rightarrow -\frac{2}{\lambda }=3$
$\Rightarrow \lambda =-\frac{2}{3}.$