Find the roots of the quadratic equation $\sqrt{3}{x}^2-2x-\sqrt{3}=0$.

We have been given the quadratic equation $\sqrt{3}{x}^2-2x-\sqrt{3}=0$  and we need to find its roots.

Factorising by splitting the middle term, we get

Taking terms common,

$\begin{array}{r}\Rightarrow \sqrt{3}x(x-\sqrt{3})+1(x-\sqrt{3})=0\\ \Rightarrow (x-\sqrt{3})(\sqrt{3}x+1)=0\\ \Rightarrow x-\sqrt{3}=0\text{ or, }\\ (\sqrt{3}x+1)=0\\ \Rightarrow x=\sqrt{3}\text{ or }\frac{-1}{\sqrt{3}}\end{array}$