Short-Answer Questions

$\sqrt{3} x^{2}+10 x-8 \sqrt{3}=0$

$\Rightarrow \sqrt{3} x^{2}+12 x-2 x-8 \sqrt{3}=0$

$\Rightarrow \sqrt{3} x(x+4 \sqrt{3})-2(x+4 \sqrt{3})=0$

$\Rightarrow(x+4 \sqrt{3})(\sqrt{3} x-2)=0$

$\Rightarrow x+4 \sqrt{3}=0$ or $\sqrt{3} x-2=0$

$\Rightarrow x=-4 \sqrt{3}$ or $x=\frac{2}{\sqrt{3}}=\frac{2 \sqrt{3}}{3}$

Hence, $-4 \sqrt{3}$ and $\frac{2 \sqrt{3}}{3}$ are the roots of the given equation.