Question

Objective Questions (MCQ)

The roots of the quadratic equation $2x^2-x-6=0$ are

(a) $-2,\frac{3}{2}$ (b) $2,\frac{-3}{2}$ (c) $-2,\frac{-3}{2}$ (d) $2,\frac{3}{2}$ [CBSE 2012]

Answer 1

The given quadratic equation is $2x^2-x-6=0$.

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

Hence, the correct answer is option B.