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

Mar 18, 2017

Zeros are $\frac{1}{3}$ and $- 1$

#### Explanation:

Observe that in quadratic function $f \left(x\right) = 3 {x}^{2} + 2 x - 1$, the discriminant ${b}^{2} - 4 a c = {2}^{2} - 4 \times 3 \times \left(- 1\right) = 16$ is a perfect square and hence, we can factorize it with rational factors,

$f \left(x\right) = 3 {x}^{2} + 2 x - 1$

= $3 {x}^{2} + 3 x - x - 1$

= $3 x \left(x + 1\right) - 1 \left(x + 1\right)$

= $\left(3 x - 1\right) \left(x + 1\right)$

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

i.e. they are $\frac{1}{3}$ and $- 1$