Question:
Very-Short-Answer Questions
Find the solution of the quadratic equation $3 \sqrt{3} x^{2}+10 x+\sqrt{3}=0$.
Solution:
The given quadratic equation is $3 \sqrt{3} x^{2}+10 x+\sqrt{3}=0$.
$3 \sqrt{3} x^{2}+10 x+\sqrt{3}=0$
$\Rightarrow 3 \sqrt{3} x^{2}+9 x+x+\sqrt{3}=0$
$\Rightarrow 3 \sqrt{3} x(x+\sqrt{3})+1(x+\sqrt{3})=0$
$\Rightarrow(x+\sqrt{3})(3 \sqrt{3} x+1)=0$
$\Rightarrow x+\sqrt{3}=0$ or $3 \sqrt{3} x+1=0$
$\Rightarrow x=-\sqrt{3}$ or $x=-\frac{1}{3 \sqrt{3}}=-\frac{\sqrt{3}}{9}$
Hence, $-\sqrt{3}$ and $-\frac{\sqrt{3}}{9}$ are the solutions of the given equation.
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