Question

Find the roots of following quadratic equation

$9s^2-4=-6s$

• A. $s=\frac{-1\pm \sqrt{5}}{3}$
• B. $s=\frac{-1\pm \sqrt{5}}{2}$
• C. $s=\frac{-5\pm \sqrt{5}}{3}$
• D. $s=\frac{-1\pm \sqrt{5}}{4}$

Answer 1

The correct option is A $s=\frac{-1\pm \sqrt{5}}{3}$

Given equation is,

$9s^2-4=-6s$
$9s^2+6s-4=0$
Using quadratic formula,

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
$a=9,b=6,c=-4$

$x=\frac{-6\pm \sqrt{36-4(-4)\left(9\right)}}{2\times 9}$
$x=\frac{-6\pm \sqrt{180}}{18}$
$x=\frac{-6\pm 6\sqrt{5}}{18}$
$\therefore x=\frac{-1\pm \sqrt{5}}{3}$

$\therefore$ roots of the given equation are $\frac{-1\pm \sqrt{5}}{3}$