question_answer

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

Answer:

Since \[x=\frac{-1}{2}\] is a solution of \[3{{x}^{2}}+2kx-3=0\] it must satisfy the equation.

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

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

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

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