Question

Solve the given quadratic equation by factorization method
$\sqrt{3}{x}^2+10x+7\sqrt{3}=0$

Answer 1

Given : $\sqrt{3}{x}^2+10x+7\sqrt{3}=0$
$\Rightarrow \sqrt{3}{x}^2+3x+7x+7\sqrt{3}=0\Rightarrow \sqrt{3}x(x+\sqrt{3})+7(x+\sqrt{3})=0\Rightarrow (x+\sqrt{3})(\sqrt{3}x+7)=0\Rightarrow x+\sqrt{3}=0or\sqrt{3}x+7=0$

$\Rightarrow x=-\sqrt{3}orx=\frac{-7}{\sqrt{3}}$

Thus, $x=-\sqrt{3}$ and $x=\frac{-7}{\sqrt{3}}$ are the two roots of the given equation.