# How do you use the rational root theorem to list all possible roots for #5x^3-11x^2+7x-1=0#?

##### 1 Answer

The "possible" rational roots are:

The actual zeros are:

#### Explanation:

By the rational root theorem, the only possible *rational* zeros of

That means that the only possible *rational* zeros are:

#+-1/5# ,#+-1#

There could be other zeros, but they will be irrational or non-Real Complex. The rational root theorem only tells us possible *rational* zeros.

Note that the sum of the coefficients of

#5-11+7-1 = 0#

So

#5x^3-11x^2+7x-1 = (x-1)(5x^2-6x+1)#

The same is true of the remaining quadratic:

#5 - 6 + 1 = 0#

So we have another zero

#5x^2-6x+1 = (x-1)(5x+1)#

The remaining factor