NCERT Class X Chapter 4: Quadratic Equation Example 5

Question:

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

Given:

The quadratic equation: 3x² - 2√6x - 2 = 0

To Find:

The roots of the equation.

Formula:

WKT, 2√ax = √ax + √ax

Solution:

The given equation is 3x² - 2√6x - 2 = 0.

Split the middle term: using the formula 2√ax = √ax+ √ax

⇒ 3x² - 2√6x - 2 = 3x² - (√6x + √6x) - 2

⇒ 3x² - 2√6x - 2 = 3x² - √6x - √6x - 2

Grouping common factors in 3x² - √6x - √6x - 2 we have

⇒ (3x² - √6x) + (- √6x - 2) = √3x(√3x-√2) -√2(√3x-√2)

⇒ 3x² - 2√6x - 2 = (√3x-√2) (√3x-√2)

Since 3x² - 2√6x - 2 = 0, (√3x-√2) (√3x-√2) = 0

Case 1:
⇒ (√3x-√2) = 0 ⇒ √3x = √2
⇒ x = √2 √3

Case 2:
⇒ (√3x-√2) = 0 ⇒ √3x = √2
⇒ x = √2 √3

Therefor the two roots are:

x = √2 √3  ,√2 √3

Result:

The roots of the equation 3x² - 2√6x - 2 = 0 are x = √2 √3 and x = √2 √3 .
The roots are equal.

Next Question Solution:

NCERT Class X Chapter 4: Quadratic Equation Example 6.

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