# Objective Questions (MCQ)

Question:

Objective Questions (MCQ)

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

(a) $-2, \frac{3}{2}$

(b) $2, \frac{-3}{2}$

(c) $-2, \frac{-3}{2}$

(d) $2, \frac{3}{2}$

Solution:

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

$2 x^{2}-x-6=0$

$\Rightarrow 2 x^{2}-4 x+3 x-6=0$

$\Rightarrow 2 x(x-2)+3(x-2)=0$

$\Rightarrow(x-2)(2 x+3)=0$

$\Rightarrow x-2=0$ or $2 x+3=0$

$\Rightarrow x=2$ or $x=\frac{-3}{2}$

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

Hence, the correct answer is option B.