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

Given: $x=-\frac{1}{2}$ is a solution of the quadratic equation $3x^{2}+2kx-3=0$.

To do: To find the value of $k$.

Solution:

As given $x=-\frac{1}{2}$ is a solution of the quadratic equation $3x^{2}+2kx-3=0$

Then $x=-\frac{1}{2}$ will satisfy the equation, On substituting $x=-\frac{1}{2}$ in the given equation

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

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

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

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

Thus, $k=-\frac{9}{4}$

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Updated on: 10-Oct-2022

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