The roots of the quadratic equation  $$3x^2 - 2\sqrt{6}x + 2 = 0$$​ are:

Correct option is C

Given:

Given equation =$$3x^2 - 2\sqrt{6}x + 2 = 0$$​​

Formula Used:

For finding the roots of equation $$ax^2 +bx +c =0$$​ we use:

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

Solution:

Given equation =$$3x^2 - 2\sqrt{6}x + 2 = 0$$​​

​$$x =\frac{ -(-2\sqrt{6}) \pm \sqrt{(-2\sqrt{6})^2 - 4(3)(2)}}{2(3)}$$​​

​$$= \frac{ 2\sqrt{6} \pm \sqrt{24 - 24}}{2(3)}$$​​

​$$= \frac{2\sqrt{6}}{6}$$​​

​$$= \frac{\sqrt{6}}{3}$$​​

​$$= \frac{ \sqrt{2 \times 3}}{\sqrt{3} \times \sqrt{3}}$$​​

​$$= \frac{\sqrt{2}}{\sqrt{3}}$$ = $$\sqrt{\frac{2}{3}}$$​​

Hence option (c) is correct