Question

Solve each of the following quadratic equations:

$x^2-\left(\sqrt{3}+1\right)x+\sqrt{3}=0$ [CBSE 2015]

Answer 1

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