Question

Find the roots of the following quadratic equation 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

6x² + 5x – 6 = 0

⇒ 6x² + (9x – 4x) – 6 = 0   ....[By splitting the middle term]

⇒ 6x² + 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 6x² + 5x – 6 = 0 are `(-3)/2` and `2/3`.