Question

Find the roots of the equation $\sqrt{3}{x}^2+11x+6\sqrt{3}=0$ by using Quadratic Formula.

Answer 1

$\sqrt{3}{x}^2+11x+6\sqrt{3}=0$

$a=\sqrt{3},b=11,c=6\sqrt{3}$

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

$x=\frac{-11\pm \sqrt{{11}^2-4\sqrt{3}6\sqrt{3}}}{2\sqrt{3}}$

$=\frac{-11\pm \sqrt{49}}{2\sqrt{3}}$

$=\frac{-11\pm 7}{2\sqrt{3}}$

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