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Rot til en ligning

Røtter av en funksjon.

I matematikk er roten til en ligning der den ukjente er et reelt eller et komplekst tall det samme som løsningen av ligningen. En ligning kan ha én eller flere røtter.

Dersom ligningen har forma , er roten til ligningen sammenfallende med nullpunktene til funksjonen . En skiller ofte ikke klart mellom de to begrepene rot og nullpunkt.

Algebraens fundamentalteorem sier at en ligning der er et n-te-gradspolynom har komplekse røtter. For en potensligning på formen vil en rot være like n-te-roten av .

Multiplisitet

[rediger | rediger kilde]

For en polynomligning av grad n på forma vil en rot ha multiplisitet m dersom polynomet kan skrives

der er et polynom av grad (nm).

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Rot til en ligning
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