Question

solve the quadratic equation 2 X ^2 + 5 √ 3 X + 6 = 0 by using quadratic formula

Answer 1

Given :

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

Comparing this with :

$ax^2+bx+c=0$

$a = 2$

$b=5\sqrt{3}$

$c=6$

$b^2-4ac=(5\sqrt{3})^2-4\times2\times6$

                  $\implies 75-48$

                  $\implies27$.....................(1)

By quadratic formula we know that :

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

$\implies x=\frac{-(-5\sqrt{3})\pm\sqrt{27}}{2\times2}$ [From (1)]

$\implies x=\frac{5\sqrt{3}\pm3\sqrt{3}}{4}$

Either :

$\implies x=\frac{5\sqrt{3}+3\sqrt{3}}{4}$

$\implies x=\frac{8\sqrt{3}}{4}$

$\implies x=2\sqrt{3}$

$\implies x=2\times1.732$

$\implies x=3.464$

Or:

$\implies x=\frac{5\sqrt{3}-3\sqrt{3}}{4}$

$\implies x=\frac{2\sqrt{3}}{4}$

$\implies x=\frac{\sqrt{3}}{2}$

$\implies x=0.866$

The values of x are : $\boxed{3.464\:\:\bf{or}\:\:0.866}$

Hope it helps you

_________________________________________________________________