Since I explored and solved this over a couple of days when this was in the queue - it was relevant to what my class was studying - I won't give the solution.
The cool thing (which is easy to show) is whenever a polynomial has terms that are "palindromic" the roots come in pairs that are reciprocals.
ax^n + bx^(n-1) + cx^(n-2) + ... + cx^2 + bx + a
Posted by Jer
on 2015-04-04 14:52:45