Find the roots of the quadratic equation $3x^{2}-2\sqrt{6}x+2=0$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The given quadratic equation is $3x^{2}-2\sqrt{6}x+2=0$.
We can factorize the middle term $-2\sqrt{6}x$ as $-\sqrt{6}x - \sqrt{6}x$.
So,$3x^{2}-\sqrt{6}x-\sqrt{6}x+2=0$.
Taking common terms from the first two and last two terms:
$\sqrt{3}x(\sqrt{3}x-\sqrt{2})-\sqrt{2}(\sqrt{3}x-\sqrt{2})=0$.
This simplifies to $(\sqrt{3}x-\sqrt{2})(\sqrt{3}x-\sqrt{2})=0$.
Setting each factor to zero,we get $\sqrt{3}x-\sqrt{2}=0$,which implies $x = \frac{\sqrt{2}}{\sqrt{3}} = \sqrt{\frac{2}{3}}$.
Since both factors are identical,the roots are equal.
Therefore,the roots of the equation are $\sqrt{\frac{2}{3}}, \sqrt{\frac{2}{3}}$.

Explore More

Similar Questions

Is it possible to design a rectangular mango grove whose length is twice its breadth,and the area is $800 \, m^2$? If so,find its length and breadth.

Find the values of $k$ for the following quadratic equation,so that it has two equal roots:
$k x(x-2)+6=0$

Find the roots of the following quadratic equation by factorisation:
$2x^{2} - x + \frac{1}{8} = 0$

Find the roots of the equation $5x^{2}-6x-2=0$ by the method of completing the square.

Difficult
View Solution

Find the discriminant of the equation $3x^{2}-2x+\frac{1}{3}=0$ and hence find the nature of its roots. Find them,if they are real.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo