Question

If $x=\frac{-1}{2}$, is a solution of the quadratic equation $3x^2+2kx-3=0$, find the value of $k$.

Answer 1

$x=\frac{-1}{2}$ is a solution of equation : $3x^2+2kx-3=0$

Let the other roots be $\alpha$.

then sum of roots = $-\frac{b}{a}=\frac{-2k}{3}=\frac{-1}{2}+\alpha$

product of roots = $\frac{c}{a}=\frac{-3}{3}=-1=\frac{-1}{2}\times \alpha$

$+1=+\frac{\alpha }{2}\Rightarrow \alpha =2$

placing in (1) $\Rightarrow \frac{-2k}{3}=\frac{-1}{2}+2=\frac{3}{2}$

$\frac{-2k}{3}=\frac{3}{2}\Rightarrow k=\frac{-9}{4}$