Question:
$\sqrt{3} x^{2}+11 x+6 \sqrt{3}=0$
Solution:
Given :
$\sqrt{3} x^{2}+11 x+6 \sqrt{3}=0$
$\Rightarrow \sqrt{3} x^{2}+9 x+2 x+6 \sqrt{3}=0$
$\Rightarrow \sqrt{3} x(x+3 \sqrt{3})+2(x+3 \sqrt{3})=0$
$\Rightarrow(x+3 \sqrt{3})(\sqrt{3} x+2)=0$
$\Rightarrow x+3 \sqrt{3}=0$ or $\sqrt{3} x+2=0$
$\Rightarrow x=-3 \sqrt{3}$ or $x=\frac{-2}{\sqrt{3}}=\frac{-2 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}=\frac{-2 \sqrt{3}}{3}$
Hence, the roots of the equation are $-3 \sqrt{3}$ and $\frac{-2 \sqrt{3}}{3}$.
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