Question

Short-Answer Questions

Solve: $4\sqrt{3}{x}^2+5x-2\sqrt{3}=0$ [CBSE 2013]

Answer 1

$$\begin{gathered} 4\sqrt{3}{x}^2+5x-2\sqrt{3}=0 \\ \Rightarrow 4\sqrt{3}{x}^2+8x-3x-2\sqrt{3}=0 \\ \Rightarrow 4x\left(\sqrt{3}x+2\right)-\sqrt{3}\left(\sqrt{3}x+2\right)=0 \\ \Rightarrow \left(\sqrt{3}x+2\right)\left(4x-\sqrt{3}\right)=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow \sqrt{3}x+2=0\mathrm{or}4x-\sqrt{3}=0 \\ \Rightarrow x=-\frac{2}{\sqrt{3}}=-\frac{2\sqrt{3}}{3}\mathrm{or}x=\frac{\sqrt{3}}{4} \end{gathered}$$

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