Question

Find the root of the following quadratic equations by the factorisation method:

`2x^2 + 5/3x - 2` = 0

Answer 1

Given equation is `2x^2 + 5/3x - 2` = 0

On multiplying by 3 on both sides, we get

`6x^2 + 5x - 6` = 0

⇒ `6x^2 + (9x - 4x) - 6` = 0   ......[By splitting the middle term]

⇒ `6x^2 + 9x - 4x - 6` = 0

⇒ `3x(2x + 3) - 2(2x + 3)` = 0

 `(2x + 3)(3x - 2)` = 0

Now, `2x + 3` = 0

⇒ `x = - 3/2`

And `3x - 2` = 0

⇒ `x = 2/3`

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