# How do you use the rational root theorem to find the roots of #x^3-x^2-x-3=0#?

##### 1 Answer

The theorem states that the polynomial has no rational roots.

#### Explanation:

The rational root theorem states that if you have a polynomial with integer coefficients (as you have), then a solution

Since in your case the leading coefficient is the coefficient of

So, we can check these four values, because we know what if there's a solution, it must be one of these four.

Let

#p(-3)=(-3)^3 - (-3^2) - (-3) -3 = #

#p(-1)=(-1)^3 - (-1^2) - (-1) -3 = -1-1+1-3 = -4 ne 0# #p(1)=1^3 -1^2 - 1 -3 = 1-1-1-3 = -4 ne 0 # #p(3)=3^3 -3^2 - 3 -3 = 27-9-3-3 = 12 ne 0 #

This means that the polynomial has no rational roots.