# How do you find all possible rational zeros of #f(x) = 2x^3 - 5x^2 + 3x - 1#?

##### 1 Answer

May 27, 2016

#### Answer:

Use the rational root theorem to help find that it has no rational zeros.

#### Explanation:

By the rational root theorem, any rational zeros of

That means that the only possible rational zeros are:

#+-1/2# ,#+-1#

In addition, note that there are no changes of signs of coefficients in

That leaves possible rational zeros:

#1/2# ,#1#

Then we find:

#f(1/2) = 1/4-5/4+3/2-1 = -1/2#

#f(1) = 2-5+3-1 = -1#

So this cubic has no rational zeros.