Question

Solve the following quadratic equation:

`4sqrt(6)x^2 - 13x - 2sqrt(6) = 0`

Answer 1

Given:

`4sqrt(6)x^2 - 13x - 2sqrt(6) = 0` 

⇒ `4sqrt(6)x^2 - 16x + 3x - 2sqrt(6) = 0` 

⇒ `4sqrt(2)x(sqrt(3)x - 2sqrt(2)) + sqrt(3)(sqrt(3)x - 2sqrt(2)) = 0`  

⇒ `(4sqrt(2)x + sqrt(3))(sqrt(3)x - 2sqrt(2)) = 0` 

⇒ `4sqrt(2)x + sqrt(3) = 0` or `sqrt(3)x - 2sqrt(2) = 0` 

⇒ `x = (-sqrt(3))/(4sqrt(2))= (-sqrt(3) xx sqrt(2))/(4sqrt(2) xx sqrt(2)) = (-sqrt(8))/8` or `x = (2sqrt(2))/sqrt(3) = (2sqrt(2) xx sqrt(3))/(sqrt(3) xx sqrt(3)) = (2sqrt(6))/3` 

Hence, the roots of the equation are `-sqrt(6)/8` and `(2sqrt(6))/3`.