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The 11 pages that link to Multiplicity of a root, each with the reason it gives.

• Polynomial factorizationRelated: Repeated factors reveal roots whose multiplicity affects graphs and algebraic calculations.

• Polynomial rootRelated: Multiplicity distinguishes repeated roots from roots that occur once.

• Discriminant (polynomial)Related: The discriminant vanishes when at least one root has multiplicity greater than one.

• Polynomial equationRelated: Repeated roots affect the root count without adding distinct solutions.

• Factor theoremRelated: Once a root is confirmed, division can test whether its factor occurs repeatedly.

• Descartes' rule of signsRelated: Roots are counted with multiplicity when comparing the bound with actual positive roots.

• Gauss–Lucas theoremRelated: Repeated roots contribute repeated terms to the logarithmic-derivative identity.

• Budan's theoremRelated: Budan's variation difference bounds roots counted with multiplicity, hence also distinct roots.

• Complex conjugate root theoremRelated: Conjugate roots occur with equal multiplicity, not merely as a pair of distinct values.

• Casas-Alvero conjectureRelated: The conjectured conclusion is that one root has multiplicity equal to the polynomial's degree.