Question

The roots of the quadratic equation 2x² − x − 6 = 0
(a) $-2,\frac{3}{2}$
(b) $2,-\frac{3}{2}$
(c) $-2,-\frac{3}{2}$
(d) $2,\frac{3}{2}$

Answer 1

$$\begin{gathered} 2x^2-x-6=0 \\ \Rightarrow 2x^2-4x+3x-6=0 \\ \Rightarrow 2x\left(x-2\right)+3\left(x-2\right)=0 \\ \Rightarrow \left(x-2\right)\left(2x+3\right)=0 \\ \Rightarrow \left(x-2\right)=0\mathrm{or}\left(2x+3\right)=0 \\ \Rightarrow x=2\mathrm{or}x=-\frac{3}{2} \end{gathered}$$

Hence, the correct answer is option (b).