Question

Find the roots of the quadratic equations $\sqrt{3}{x}^2-2\sqrt{2}x-2\sqrt{3}=0$.

Answer 1

Given ${\sqrt{3x}}^2-2\sqrt{2x}-2\sqrt{3}=0---\left(1\right)$

using discriminant.

D$=b^2-4ac=8+24=32$

now x $=\frac{-b+\sqrt{D}}{2a}=\frac{2\sqrt{2}+\sqrt{32}}{2\sqrt{3}}$

$x=\frac{2\sqrt{2}+4\sqrt{2}}{2\sqrt{3}}$=$3\sqrt{\frac{2}{3}},-\sqrt{\frac{2}{3}}.$

$\therefore$ roots of given equation are $3\sqrt{\frac{2}{3}}$ $-\sqrt{\frac{2}{3}}$