Theorems · Theorem · field theory
Polynomial.roots_C_mul_X_add_C_of_IsUnit
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R] (b : R) (a : Rˣ),
(Polynomial.C ↑a * Polynomial.X + Polynomial.C b).roots = {-(↑a⁻¹ * b)}- Defined in
- Mathlib.Algebra.Polynomial.Roots
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Unitsstatement and proof · cited by 2,804
- Multisetstatement and proof · cited by 2,627
- IsDomainstatement and proof · cited by 2,196
- Units.valstatement and proof · cited by 1,966
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- mul_negproof · cited by 590
- sub_neg_eq_addproof · cited by 264
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.roots_C_mul_X_add_Cproof · cited by 1