Question

4 root 3 x2 + 5x - 2 root 3 = 0 find the roots of the following quadratic equation by the factorisation method

Answer 1

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