Question

Solve the following equation by factorization:

`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`

⇒ `(sqrt(3)x + 2)(x + 3sqrt(3)) = 0`

⇒ `(sqrt(3)x + 2) = 0` or `(x + 3sqrt(3)) = 0`   ...[Using zero-product rule]

⇒ `sqrt(3)x = -2` or `x = -3sqrt(3)`

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

Hence, `x = {(-2)/sqrt(3), -3sqrt(3)}`.