Question

Find the root of the following quadratic equations 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)`.