Question

How do you solve and write the following in interval notation: `3a - 6a^2 >0`?

Answer 1

Solution : `0 < a < 1/2`. In interval notation: `(0 , 1/2)`.

Explanation:

`3a -6a^2 >0 or 3a(1-2a) > 0 or a(1-2a) >0`

Critical points are `a=0` and `a=1/2`

When `a < 0 , a (1-2a) < 0` (1)
When `0 < a < 1/2 , a (1-2a) > 0` (2)
When `a >1/2 , a (1-2a) < 0` (3)

Solution : `0 < a < 1/2`. In interval notation: `(0,1/2)`. In graph also `3a-6a^2>0` for `0 < a < 1/2` graph{-6x^2+3x [-10, 10, -5, 5]} [Ans]