Question

In the following, determine the value of $k$ for which the given value is a solution of the equation.
$3x^2+2kx-3=0,x=-\frac{1}{2}$

Answer 1

Since $x=\frac{-1}{2}$ is a root of the given equation. So, it satisfies the equation

i.e., $3{(-\frac{1}{2})}^2+2k(-\frac{1}{2})-3=0\Rightarrow \frac{3}{4}-k-3=0$

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