proposition: Lemma rootsZ a b c p : c != 0 -> roots (c *: p) a b = roots p a b.
proof: Proof. case: (eqVneq p 0) => [->|p_neq0 c_neq0]; first by rewrite scaler0. by apply/roots_eq => [||x axb]; rewrite ?scaler_eq0 ?(negPf c_neq0) ?rootZ. 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)