Ivan Shishkin, Rye (1878)

Problems/General algebraUnreviewed

Des irrationnels

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Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Soit P∈Q[X]P \in \mathbb{Q}[X] irréductible de degré ⩾3\geqslant 3 qui admet exactement deux racines non réelles conjuguées zz et zˉ\bar{z}. Montrer que Im⁡(z)∉Q\Im(z) \notin \mathbb{Q}.

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