Find the roots of the quadratic equation 3x² - 2√6x + 2 = 0

Solution :

Let us find the roots by splitting the middle term.

Given, 3x² - 2√6x + 2 = 0

Split bx into such a way that it is equal to a×c.

- 2√6x can be split into- √6x and - √6x . [ ∵ (- √6x) × (- √6x) = 6x²]. 

⇒ 3x² - 2√6x + 2 = 0 can be written as 3x² - √6x - √6x + 2 = 0.

Take out the common factors,

⇒ √3x (√3x - √2) - √2 (√3x - √2)

⇒ (√3x - √2)(√3x - √2) 

Put both the equations equal to 0

⇒ √3x - √2 = 0 and √3x - √2 = 0

⇒ x = √⅔ 

Since the roots are repeated twice, the roots of the equation are √⅔ , √⅔

☛ Check: NCERT Solutions for Class 10 Maths Chapter 4

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Find the roots of the quadratic equation 3x² - 2√6x + 2 = 0

Summary:

The roots of the quadratic equation 3x² - 2√6x + 2 = 0 are √⅔

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