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.
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