Short-Answer Questions

$\sqrt{3} x^{2}-2 \sqrt{2} x-2 \sqrt{3}=0$

$\Rightarrow \sqrt{3} x^{2}-3 \sqrt{2} x+\sqrt{2} x-2 \sqrt{3}=0$

$\Rightarrow \sqrt{3} x(x-\sqrt{6})+\sqrt{2}(x-\sqrt{6})=0$

$\Rightarrow(x-\sqrt{6})(\sqrt{3} x+\sqrt{2})=0$

$\Rightarrow x-\sqrt{6}=0$ or $\sqrt{3} x+\sqrt{2}=0$

$\Rightarrow x=\sqrt{6}$ or $x=-\frac{\sqrt{2}}{\sqrt{3}}=-\frac{\sqrt{6}}{3}$

Hence, $\sqrt{6}$ and $-\frac{\sqrt{6}}{3}$ are the roots of the given equation.