Question

Solve the following quadratic equation:

`x^2 + 3sqrt(3)x - 30 = 0`

Answer 1

We write, `3sqrt(3)x = 5sqrt(3)x - 2sqrt(3)x` as `x^2 xx (-30) = -30x^2 = 5sqrt(3)x xx (-2sqrt(3)x)`  

∴ `x^2 + 3sqrt(3)x - 30 = 0` 

⇒ `x^2 + 5sqrt(3)x - 2sqrt(3)x - 30 = 0` 

⇒ `x(x + 5sqrt(3)) - 2sqrt(3)(x + 5sqrt(3)) = 0` 

⇒ `(x + 5sqrt(3)) (x - 2sqrt(3)) = 0` 

⇒ `x + 5sqrt(3) = 0` or `x - 2sqrt(3) = 0` 

⇒ `x = -5sqrt(3)` or `x = 2sqrt(3)` 

Hence, the roots of the given equation are `-5sqrt(3)` and `2sqrt(3)`.