proposition: Lemma rootsC (a b c : R) : roots c%:P a b = [::].
proof: Proof. have [->|hc] := eqVneq c 0; first by rewrite roots0. by apply: no_root_roots=> x hx; rewrite rootC. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq choice fintype) mathcomp(bigop order ssralg poly polydiv ssrnum zmodp) mathcomp(polyorder path interval ssrint)