Question

If $\sqrt{\frac{2}{3}}$ is a solution of equation $3x^2+mx+2=0$. Find the value of $m$.

Answer 1

Step : Finding the value of $m$.

$\sqrt{\frac{2}{3}}$ is solution of $3x^2+mx+2=0$
Therefore,
$3\times {\left(\sqrt{\frac{2}{3}}\right)}^2+m\times \sqrt{\frac{2}{3}}+2=0$
$\Rightarrow 3\times \frac{2}{3}+\sqrt{\frac{2}{3}}m+2=0$
$\Rightarrow m\times \sqrt{\frac{2}{3}}=-4$
$\Rightarrow m=-4\sqrt{\frac{3}{2}}$
$\Rightarrow m=-2\sqrt{6}$