different between polynomial vs discriminant

English

Etymology

poly- +? -nomial, from ????? (nomós, “portion, part”), by analogy with binomial.

Noun

polynomial (plural polynomials)

1. (algebra, strict sense) An expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power, such as ${\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{0}x^{0}}$.
2. (taxonomy) A taxonomic designation (such as of a subspecies) consisting of more than two terms.

Hyponyms

• binomial
• homogeneous polynomial
• monomial
• trinomial
• quadrinomial
• quantic

Holonyms

• rational function

Derived terms

Translations

Adjective

polynomial (not comparable)

1. (algebra) Able to be described or limited by a polynomial.
2. (taxonomy) of a polynomial name or entity

Translations

See also

• Appendix:English polynomial degrees

French

Adjective

polynomial (feminine singular polynomiale, masculine plural polynomiaux, feminine plural polynomiales)

1. polynomial

Related terms

• polynôme

English

Noun

discriminant (plural discriminants)

1. (algebra) An expression that gives information about the roots of a polynomial; for example, the expression D = b² - 4ac determines whether the roots of the quadratic equation ax² + bx + c = 0 are real and distinct (D > 0), real and equal (D = 0) or complex (D < 0).
2. (geometry) The invariant (on the vector space of forms of degree d in n variables) that vanishes exactly when the corresponding hypersurface in P^n-1 is singular.

Derived terms

Translations

Adjective

discriminant (comparative more discriminant, superlative most discriminant)

1. Serving to discriminate.

Catalan

Verb

discriminant

1. present participle of discriminar

Dutch

Etymology

Borrowed from Latin discr?min?ns.

Pronunciation

• IPA^(key): /?d?s.kri.mi?n?nt/
• Hyphenation: dis?cri?mi?nant
• Rhymes: -?nt

Noun

discriminant m (plural discriminanten, diminutive discriminantje n)

1. (algebra) discriminant

French

Pronunciation

• IPA^(key): /dis.k?i.mi.n??/

Noun

discriminant m (plural discriminants)

1. (mathematics) discriminant

Further reading

• “discriminant” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

Latin

Verb

discr?minant

1. third-person plural present active indicative of discr?min?

Romanian

Etymology

From French discriminant.

Adjective

discriminant m or n (feminine singular discriminant?, masculine plural discriminan?i, feminine and neuter plural discriminante)

1. discriminant

Declension