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

The sum of squares of two consecutive odd numbers is $514$. Find those numbers.

Difficult
View Solution

Solve the following equation using the method of factorization: $\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6} \,(x \neq 3, -5)$

Difficult
View Solution

The roots of $4x^{2} + 2x + \frac{1}{4} = 0$ are $\ldots \ldots \ldots \ldots.$

The roots of the quadratic equation $3x^2 - 4x + 1 = 0$ are:

Solve the following equation using the method of factorization and write its solution set: $\frac{x+1}{x+2} + \frac{1}{x} = \frac{5}{4}$

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