Question

Very-Short-Answer Questions

Find the roots of the quadratic equation $2x^2-x-6=0$. [CBSE 2012]

Answer 1

The given quadratic equation is $2x^2-x-6=0$.
$$\begin{gathered} 2x^2-x-6=0 \\ \Rightarrow 2x^2-4x+3x-6=0 \\ \Rightarrow 2x\left(x-2\right)+3\left(x-2\right)=0 \\ \Rightarrow \left(x-2\right)\left(2x+3\right)=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow x-2=0\mathrm{or}2x+3=0 \\ \Rightarrow x=2\mathrm{or}x=-\frac{3}{2} \end{gathered}$$
Hence, the roots of the given equation are 2 and $-\frac{3}{2}$.