Solve this
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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