Question

Find the roots of the following quadratic equation by the factorisation method:

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

Answer 1

Given equation is `3sqrt(2)x^2 - 5x - sqrt(2)` = 0

⇒ `3sqrt(2) x^2 - (6x - x) - sqrt(2)` = 0  ....[By splitting the middle term]

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

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

⇒ `3sqrt(2)x (x - sqrt(2)) + 1(x - sqrt(2))` = 0

⇒ `(x - sqrt(2))(3sqrt(2)x + 1)` = 0

Now, `x - sqrt(2)` = 0

⇒ x = `sqrt(2)`

And `3sqrt(2)x + 1` = 0

⇒ x = `-1/(3sqrt(2)) = (-sqrt(2))/6`

Hence, the roots of the equation `3sqrt(2)x^2 - 5x - sqrt(2)` = 0 are `- sqrt(2)/6` and `sqrt(2)`.