proposition: Lemma eqp_root p q : p %= q -> root p =1 root q.
proof: Proof. move/eqpP=> [[c d]] /andP [c0 d0 e] x; move/negPf:c0=>c0; move/negPf:d0=>d0. by rewrite rootE -[_==_]orFb -c0 -mulf_eq0 -hornerZ e hornerZ mulf_eq0 d0. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop ssralg poly)