Question

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

Answer 1

$\begin{array}{c}{x}^2+2\sqrt{3}x+3=0\\ \Rightarrow x^2+\sqrt{3}x+\sqrt{3}x+3=0\\ \Rightarrow x\left(x+\sqrt{3}\right)+\sqrt{3}\left(x+\sqrt{3}\right)=0\\ \Rightarrow \left(x+\sqrt{3}\right)\left(x+\sqrt{3}\right)=0\\ \Rightarrow {\left(x+\sqrt{3}\right)}^2=0\end{array}$

$\therefore$ Roots are equals and it is $\left(-\sqrt{3}\right)$.