Question

Very-Short-Answer Questions

Find the solution of the quadratic equation $3\sqrt{3}{x}^2+10x+\sqrt{3}=0$. [CBSE 2009]

Answer 1

The given quadratic equation is $3\sqrt{3}{x}^2+10x+\sqrt{3}=0$.
$$\begin{gathered} 3\sqrt{3}{x}^2+10x+\sqrt{3}=0 \\ \Rightarrow 3\sqrt{3}{x}^2+9x+x+\sqrt{3}=0 \\ \Rightarrow 3\sqrt{3}x\left(x+\sqrt{3}\right)+1\left(x+\sqrt{3}\right)=0 \\ \Rightarrow \left(x+\sqrt{3}\right)\left(3\sqrt{3}x+1\right)=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow x+\sqrt{3}=0\mathrm{or}3\sqrt{3}x+1=0 \\ \Rightarrow x=-\sqrt{3}\mathrm{or}x=-\frac{1}{3\sqrt{3}}=-\frac{\sqrt{3}}{9} \end{gathered}$$
Hence, $-\sqrt{3}$ and $-\frac{\sqrt{3}}{9}$ are the solutions of the given equation.