Question

Find the roots of the following quadratic equations by factorisation:
3x2 —2√6x +2 = 0

Answer 1

Answer:

refer to the attachment for the solution.

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Answer 2

Question:

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

Answer:

x = √(2/3) , √(2/3)

(equal roots)

Note:

• The possible values of unknown (variable) for which the equation is satisfied are called its solutions or roots .

• If x = a is a solution of any equation in x , then it must satisfy the given equation otherwise it's not a solution (root) of the equation.

Solution:

The given quadratic equation is :

3x² - 2√6x + 2 = 0 .

Now ,

Splitting the middle term of the given quadratic equation, we have ;

=> 3x² - 2√6x + 2 = 0

=> 3x² - √6x - √6x + 2 = 0

=> √3x(√3x - √2) -√2(√3x - √2) = 0

=> (√3x - √2)(√3x - √2) = 0

=> √3x - √2 = 0 or √3x - √2 = 0

=> √3x = √2 or √3x = √2

=> x = √2/√3 or x = √2/√3

=> x = √(2/3) , √(2/3)

Hence,

The roots of the given quadratic equation are equal ie , x = √(2/3) , √(2/3)