Equilibrium Points for 8th Degree Polynomial

Question

I have an 8th degree polynomial that I need the zeros for. Is there even a way to explicitly solve one? Its for a diff equations review. I need to sketch the phase line, which is a breeze once I get these points.

Answer 1

The polynomial $f(y)=y^8+3y^6+y^4+y^2-1$ has the following eight complex roots: \begin{align} y&=0.528895152153 + 0.77514139686\cdot i, \\ y&=0.528895152153 - 0.77514139686\cdot i, \\ y&=1.67802753513\cdot i,\\ y&= - 1.67802753513\cdot i, \\ y&= - 0.528895152153 + 0.77514139686\cdot i,\\ y&= - 0.528895152153 - 0.77514139686\cdot i,\\ y&=0.676760382226,\\ y&= - 0.676760382226. \end{align}