Question

$4\sqrt{3}{x}^2+5x-2\sqrt{3}=0$

Answer 1

$$\begin{gathered} \text{Given:} \\ {x}^2-(1+\sqrt{2})x+\sqrt{2}=0 \\ \Rightarrow x^2-x-\sqrt{2}x+\sqrt{2}=0 \\ \Rightarrow x(x-1)-\sqrt{2}(x-1)=0 \\ \Rightarrow (x-\sqrt{2})(x-1)=0 \\ \Rightarrow x-\sqrt{2}=0\text{or}x-1=0 \\ \Rightarrow x=\sqrt{2}\text{or}x=1 \\ \mathrm{H}\text{ence, the roots of the equation are}\sqrt{2}\text{and 1}. \end{gathered}$$