posted by Danielle .
what are the zeros for 1x^5+2x^4+4x^3+19x^2+9x^2+9x-5?
5th-degree polynomials are not open to solution in general, so look for low-hanging fruit using synthetic division.
any rational roots must be ±1 or ±5.
no joy there.
not sure how to find the roots analytically. You may have to use some iterative methods. Don't know whether you have studied those yet.
If you go to wolframalpha.com and enter
solve x^5+2x^4+4x^3+19x^2+9x^2+9x-5 = 0
you will get the roots, but not much help in figuring out the exact values using radicals.