Question

Short-Answer Questions

Solve: $3x^2+5\sqrt{5}x-10=0$ [CBSE 2014]

Answer 1

$$\begin{gathered} 3x^2+5\sqrt{5}x-10=0 \\ \Rightarrow 3x^2+6\sqrt{5}x-\sqrt{5}x-10=0 \\ \Rightarrow 3x\left(x+2\sqrt{5}\right)-\sqrt{5}\left(x+2\sqrt{5}\right)=0 \\ \Rightarrow \left(x+2\sqrt{5}\right)\left(3x-\sqrt{5}\right)=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow x+2\sqrt{5}=0\mathrm{or}3x-\sqrt{5}=0 \\ \Rightarrow x=-2\sqrt{5}\mathrm{or}x=\frac{\sqrt{5}}{3} \end{gathered}$$

Hence, $-2\sqrt{5}$ and $\frac{\sqrt{5}}{3}$ are the roots of the given equation.