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

Since, $x=-\frac{1}{2}$, is a solution of the quadratic equation $3x^2+2kx-3=0$.
So, it satisfies the given equation.

$$\begin{gathered} \therefore 3{\left(-\frac{1}{2}\right)}^2+2k\left(-\frac{1}{2}\right)-3=0 \\ \Rightarrow \frac{3}{4}-k-3=0 \\ \Rightarrow k=\frac{3}{4}-3 \\ \Rightarrow k=\frac{3-12}{4} \\ \Rightarrow k=-\frac{9}{4} \end{gathered}$$

Thus, the value of k is $-\frac{9}{4}$.