Question

Obtain the roots of the following quadratic equation by using the general formula the solution:
$2x^2+5\sqrt{3}x+6=0$

Answer 1

Formula:

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

Given,

$2x^2+5\sqrt{3}x+6=0$

$x=\frac{-5\sqrt{3}\pm \sqrt{{\left(5\sqrt{3}\right)}^2-4\cdot 2\cdot 6}}{2\cdot 2}$

$=\frac{-5\sqrt{3}\pm 3\sqrt{3}}{4}$

$x=-\frac{\sqrt{3}}{2},-2\sqrt{3}$