Question

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

Answer 1

Since,  \[x = - \frac{1}{2}\],is a solution of the quadratic equation  \[3 x^2 + 2kx - 3 = 0\]

So, it satisfies the given equation.

\[\therefore 3 \left( - \frac{1}{2} \right)^2 + 2k\left( - \frac{1}{2} \right) - 3 = 0\]

\[ \Rightarrow \frac{3}{4} - k - 3 = 0\]

\[ \Rightarrow k = \frac{3}{4} - 3\]

\[ \Rightarrow k = \frac{3 - 12}{4}\]

\[ \Rightarrow k = - \frac{9}{4}\]

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