Theorems · Theorem · field theory
Polynomial.Splits.of_natDegree_eq_two
∀ {R : Type u_1} [inst : Field R] {f : Polynomial R} {x : R}, f.natDegree = 2 → Polynomial.eval x f = 0 → f.SplitsA polynomial of degree 2 with a root splits.
- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.evalstatement and proof · cited by 796
- Polynomial.Splitsstatement and proof · cited by 290
- Polynomial.divByMonicproof · cited by 77
- Polynomial.monic_X_sub_Cproof · cited by 41
- Polynomial.natDegree_X_sub_Cproof · cited by 22
- Polynomial.X_sub_C_ne_zeroproof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Splits.of_degree_eq_twoproof · cited by 0