View source for discriminant

==English==
{{wikipedia}}
{{root|en|ine-pro|*krey-}}

===Pronunciation===
* {{audio|en|LL-Q1860 (eng)-Wodencafe-discriminant.wav|a=US}}

===Noun===
{{en-noun}}

# {{lb|en|algebra}} An [[expression]] that gives information about the [[root]]s of a [[polynomial]]; for example, the [[expression]] ''D = b<sup>2</sup> - 4ac'' determines whether the [[root]]s of the [[quadratic equation]] ''ax<sup>2</sup> + bx + c = 0'' are [[real]] and [[distinct]] (''D'' > 0), real and [[equal]] (''D'' = 0) or [[complex]] (''D'' < 0).
# {{lb|en|geometry}} The [[invariant]] (on the vector space of forms of degree ''d'' in ''n'' [[variable]]s) that vanishes exactly when the corresponding [[hypersurface]] in P<sup>''n''-1</sup> is singular.

====Derived terms====
{{col-auto|en|multidiscriminant
|discriminantly
|nondiscriminant
|discriminant function
|discriminantal}}

====Translations====
{{trans-top|in algebra}}
* Chinese:
*: Cantonese: {{t|yue|[[判別式]]／[[判别式]]|tr=pun3 bit6 sik1}}
*: Mandarin: {{t+|cmn|判別式|tr=pànbiéshì}}
* Czech: {{t|cs|diskriminant|m}}
* Danish: {{t|da|diskriminant}}
* Finnish: {{t|fi|diskriminantti}}
* French: {{t+|fr|discriminant|m}}
* Greek: {{t+|el|διακρίνουσα|f}}
* Hungarian: {{t+|hu|diszkrimináns}}
* Japanese: {{t|ja|判別式|tr=hanbetsushiki}}
* Persian: {{t+|fa|مبین|tr=mobayyen}}
* Polish: {{t+|pl|wyróżnik|m}}
* Romanian: {{t+|ro|discriminant|m}}
* Russian: {{t+|ru|дискримина́нт|m}}
* Spanish: {{t|es|discriminante}}
* Swedish: {{t+|sv|diskriminant||c}}
* Tagalog: {{t|tl|talangi}}
* Thai: {{t|th|ดิสคริมิแนนต์}}
{{trans-bottom}}

===Adjective===
{{en-adj}}

# Serving to [[discriminate]].

==Catalan==

===Verb===
{{head|ca|gerund}}

# {{gerund of|ca|discriminar}}

==Dutch==

===Etymology===
Borrowed from {{bor|nl|la|discrīmināns}}.

===Pronunciation===
* {{IPA|nl|/ˌdɪs.kri.miˈnɑnt/}}
* {{audio|nl|Nl-discriminant.ogg}}
* {{hyphenation|nl|dis|cri|mi|nant}}
* {{rhymes|nl|ɑnt}}

===Noun===
{{nl-noun|m|-en|+}}

# {{lb|nl|algebra}} {{l|en|discriminant}}

==French==

===Pronunciation===
* {{fr-IPA}}
* {{audio|fr|Fr-Paris--discriminant.ogg|a=Paris}}

===Noun===
{{fr-noun|m}}

# {{lb|fr|mathematics}} {{l|en|discriminant}}

===Further reading===
* {{R:fr:TLFi}}

==Latin==

===Verb===
{{head|la|verb form|head=discrīminant}}

# {{inflection of|la|discrīminō||3|p|pres|actv|indc}}

==Romanian==

===Etymology===
{{bor+|ro|fr|discriminant}}.

===Adjective===
{{ro-adj}}

# {{l|en|discriminant}}

====Declension====
{{ro-decl-adj}}