Question

3) Solve the following quadratic equation by factorization method
$3x {}^{2} - 2 \sqrt{6x} + 2 = 0$
​

Answer 1

Required Answer:-

Given:

• 3x² - 2√6x + 2 = 0

To Find:

• The roots of the given quadratic equation.

Solution:

We have,

➡ 3x² - 2√6x + 2 = 0

We need to split -2√6 into two parts whose sum is -2√6 and product is 6.

We found,

• -√6 - √6 = -2√6
• (-√6) × (-√6) = 6

Therefore,

➡ 3x² - √6x - √6x + 2 = 0

➡ √3x(√3x - √2) - √2(√3x - √2) = 0

➡ (√3x - √2)(√3x - √2) = 0

By zero product rule,

➡ Either (√3x - √2) = 0 or (√3x - √2) = 0

➡ x = √(2/3), √(2/3)

★ Hence, the roots of the given quadratic equation are √(2/3) and √(2/3) [Equal Roots]

Answer:

• Zeros are - √(2/3), √(2/3)