Question

In the given, determine whether the given quadratic equation has real roots and if so, find the roots.
$2x^2+5\sqrt{3}x+6=0$

Answer 1

The given equation is $2x^2+5\sqrt{3}x+6=0$

Here $a=2,b=5\sqrt{3},c=6$

$\therefore D=b^2-4ac={\left(75\right)}^{}-4\times 2\times 6=27>0$

So, the given equation has real roots given by

$\alpha =\frac{-b+\sqrt{D}}{2a}=\frac{-5\sqrt{3}+\sqrt{27}}{2\times 2}=\frac{-\sqrt{3}}{2}$

$\beta =\frac{-b-\sqrt{D}}{2a}=\frac{-5\sqrt{3}-\sqrt{27}}{2\times 2}=-2\sqrt{3}$