Question

Find the roots of following quadratic equation

$2x^2-x-4=0$

• A. $x=\frac{2\pm \sqrt{33}}{4}$
• B. $x=\frac{1\pm \sqrt{33}}{4}$
• C. $x=\frac{1\pm \sqrt{33}}{2}$
• D. $x=\frac{1\pm \sqrt{22}}{4}$

Answer 1

The correct option is B $x=\frac{1\pm \sqrt{33}}{4}$

Given equation is

$2x^2-x-4=0$
Using quadratic formula,
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
$a=2,b=-1,c=-4$

$x=\frac{1\pm \sqrt{1-4(-4)\left(2\right)}}{2\times 2}$
$\therefore x=\frac{1\pm \sqrt{33}}{4}$

$\therefore$ the roots of the given equation are $\frac{1\pm \sqrt{33}}{4}$