Find the five roots

Question

What are the rational roots to five x to the 5th -15 x to the fourth minus 8X cubed +24X squared minus 4X +12?

Answer 1

If this equation has rational roots, I cannot find them.

The possible rational roots are:

12,6,4,3,2,1 divided by 1 or by 5

and the negatives of those numbers.

My graphing calculator gives me the following real roots (and there is also a pair of complex conjugate roots);

3.209756

1.636944

-.274374