Question

What are all the possible rational zeros for `f(x)=3x^2+2x-1`?

Answer 1

Zeros are `1/3` and `-1`

Explanation:

Observe that in quadratic function `f(x)=3x^2+2x-1`, the discriminant `b^2-4ac=2^2-4xx3xx(-1)=16` is a perfect square and hence, we can factorize it with rational factors,

`f(x)=3x^2+2x-1`

= `3x^2+3x-x-1`

= `3x(x+1)-1(x+1)`

= `(3x-1)(x+1)`

Hence, zeros are given by `3x-1=0` and `x+1=0`

i.e. they are `1/3` and `-1`