Question

Solve the following quadratic equation:

`sqrt(3)x^2 + 11x + 6sqrt(3) = 0`

Answer 1

Given:

`sqrt(3)x^2 + 11x + 6sqrt(3) = 0` 

⇒ `sqrt(3)x^2 + 9x + 2x + 6sqrt(3) = 0` 

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

⇒ `(x + 3sqrt(3))(sqrt(3)x + 2) = 0` 

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

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

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