Question

If $x=\frac{-1}{2}$ is solution of equation ${3x}^2+2kx-3=0$ find k

Answer 1

$p\left(x\right)=3x^2+2kx-3$

$p\left(\frac{-1}{2}\right)=3{\left(\frac{-1}{2}\right)}^2+2k\left(\frac{-1}{2}\right)-3=0$

$\Rightarrow \frac{3}{4}-k-3=0$

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

$\Rightarrow k=\frac{-9}{4}$.