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Everything about Discriminant

Function of a polynomial's coefficients that gives information about its roots

In mathematics, the discriminant of a polynomial is an expression in its coefficients that provides information about its roots without explicitly calculating them. For a polynomial with fixed coefficients, its discriminant is a fixed value: unlike the polynomial, it does not vary with the variable. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: DiscriminantA 5-minute orientation
  2. Skim a recent paper: A typology of validity: content, face, convergent, discriminant, nomological and predictive validityInfluential work since 2022
  3. Pick up a classic book: The mis-education of the NegroThe most-reprinted book on the subject
  4. Read the landmark paper: A new criterion for assessing discriminant validity in variance-based structural equation modelingCited 34,655 times
  5. Go sideways: ResultantA closely related topic
  6. Go sideways: Quadratic formA closely related topic

📖 Definitions

Noun An expression that gives information about the roots of a polynomial; for example, the expression D = b - 4ac determines whether the roots of the quadratic equation ax + bx + c = 0 are real and distinct (D > 0), real and equal (D = 0) or complex (D < 0).

Noun The invariant (on the vector space of forms of degree d in n variables) that vanishes exactly when the corresponding hypersurface in P is singular.

Adjective Serving to discriminate.

🗂️ The subject at a glance

  1. Origin
  2. Definition
  3. Low degrees
  4. Properties
  5. Real roots
  6. Homogeneous bivariate polynomial
  7. Use in algebraic geometry
  8. Generalizations

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

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