Jelly, 8 bytes
ASŒRḅ@Ðḟ
##How?
ASŒRḅ@Ðḟ || Full program (monadic link). AS || Sum the absolute values. ŒR || And create the symmetric inclusive range from its negative value. Ðḟ || And discard those that yield a truthy value... ḅ@ || When plugging them into the polynomial.
Based off Luis' answer.