# How do you use the rational roots theorem to find all possible zeros of #f(x)=x^4-x-4#?

##### 1 Answer

The rational root theorem helps us determine that this

#### Explanation:

By the rational roots theorem, any rational zeros of

That means that the only possible rational zeros are:

#+-1# ,#+-2# ,#+-4#

Trying each in turn, we find:

#f(1) = 1-1-4 = -4#

#f(-1) = 1+1-4 = -2#

#f(2) = 16-2-4 = 10#

#f(-2) = 16+2-4 = 14#

#f(4) = 256-4-4 = 248#

#f(-4) = 256+4-4 = 256#

So there are no rational zeros, but

That's as much as we can learn about this