An user French
says…

Il
👨
Pronoun
  faudra
Verb
  alors
Adverb
  distinguer
Verb
  plusieurs
Determiner
  cas
Noun
selon
Adposition
  le
Determiner
  nombre de
  racines
Noun
  du
  polynôme
Noun
  caractéristique
Adjective
.

It will then be necessary to distinguish several cases, according to the number of roots of the characteristic polynomial.
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New
il

  1. he (third-person singular masculine subject pronoun for human subject)
  2. it (third-person singular subject pronoun for grammatically masculine objects)
  3. Impersonal subject; it

New
faudra

third-person singular future indicative of falloir

New
alors

New
distinguer

  1. to distinguish
  2. to be distinguished

New
cas

  1. case, situation
  2. case
  3. case
  4. case

New
le

New
du

New
caractéristique

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