Question

Find the value of '$k$' so that the sum of the roots of equation ${3x}^2+(2x+1)x-k+5=0$ is equal to the product of roots.

• A. $4$
• B. $2$
• C. $3$
• D. $-6$

Answer 1

The correct option is D $-6$

In equation $3x^2+(2k+1)x-k+5$

We have $a=3,b=(2k+1)$ and $c=-k+5$

Then sum of roots $=$ $\alpha +\beta =\alpha \beta$
$=\frac{-(2k+1)}{3}$

And product of roots $=$ $\alpha \times \beta =\frac{-k+5}{3}$

But sum of roots= product of roots

$\therefore \frac{-(2k+1)}{3}=\frac{-k+5}{3}$

$\Rightarrow -2k-1=-k+5$

$\Rightarrow k=-6$

Then $k=-6$