Question

X2-3√3x+6=0 solve the following quadratic eqaution by factorization

Answer 1

Answer:

2√3 , √3

Step-by-step explanation:

To find ---> Roots of quadratic equation

x² - 3√3 x + 6 = 0 by factorization method

Solution---> We do factors by splitting the middle term .

First we do prime factorization of 6 and form two numbers from them whose sum is 3√3

6 = 3 × 2 × 1

= √3 × √3 × 2 × 1

= (2√3 ) ( 1√3 )

We know that

2√3 + 1√3 = 3√3

So two numbers whose product is 6 and whose sum is 3√3 are 2√3 and √3 .

Now

x² - 3 √3 x + 6 = 0

x² - ( 2√3 + √3 ) x + 6 = 0

x² - (2√3 x + √3 x ) + 6 = 0

x² - 2√3 x - √3 x + 6 = 0

x ( x - 2√3 ) - ( √3 x - 6 ) = 0

x ( x - 2√3 ) - (√3x - 2 √3 √3 ) = 0

x ( x - 2 √3 ) - √3 ( x - 2 √3 ) = 0

( x - 2 √3 ) ( x - √3 ) = 0

If x - 2√3 = 0

x = 2 √3

If x - √3 = 0

x = √3