# What are all the rational zeros of #2x^3-15x^2+9x+22#?

##### 1 Answer

Use the rational roots theorem to find the possible *rational* zeros.

#### Explanation:

#f(x) = 2x^3-15x^2+9x+22#

By the rational roots theorem, the only possible *rational* zeros are expressible in the form

So the only possible *rational* zeros are:

#+-1/2, +-1, +-2, +-11/2, +-11, +-22#

Evaluating *rational* zeros.

We can find out a little more without actually solving the cubic...

The discriminant

#Delta = b^2c^2-4ac^3-4b^3d-27a^2d^2+18abcd#

In our example,

#Delta = 18225-5832+297000-52272-106920 = 150201#

Since

Using Descartes' rule of signs, we can determine that two of these zeros are positive and one negative.