Question

Solve each of the following quadratic equations:

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

Answer 1

Consider $\sqrt{3}{x}^2+10x-8\sqrt{3}=0$
Factorising by splitting the middle term;
$$\begin{gathered} \sqrt{3}{x}^2+12x-2x-8\sqrt{3}=0 \\ \Rightarrow \sqrt{3}x(x+4\sqrt{3})-2(x+4\sqrt{3})=0 \\ \Rightarrow (\sqrt{3}x-2)(x+4\sqrt{3})=0 \\ \Rightarrow \sqrt{3}x-2=0\mathrm{or}x+4\sqrt{3}=0 \\ \Rightarrow x=\frac{2}{\sqrt{3}}\mathrm{or}x=-4\sqrt{3} \end{gathered}$$
Hence, the roots of the given equation are $\frac{2}{\sqrt{3}}$ and $-4\sqrt{3}$.