Question

Find the roots of following quadratic equation

$5m^2-2m=2$

• A. $m=\frac{1\pm \sqrt{9}}{5}$
• B. $m=\frac{-1\pm \sqrt{11}}{5}$
• C. $m=\frac{1\pm \sqrt{11}}{5}$
• D. $m=\frac{1\pm \sqrt{13}}{5}$

Answer 1

The correct option is C $m=\frac{1\pm \sqrt{11}}{5}$

Given equation is

$5m^2-2m=2$
$5m^2-2m-2=0$
Using quadratic formula,
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$a=5,b=-2,c=-2$

$x=\frac{2\pm \sqrt{4-4(-2)\left(5\right)}}{2\times 5}$

$x=\frac{2\pm \sqrt{44}}{10}$

$x=\frac{2\pm 2\sqrt{11}}{10}$

$\therefore x=\frac{1\pm \sqrt{11}}{5}$

$\therefore$ the roots of the given equation are $\frac{1\pm \sqrt{11}}{5}$