Question #6769   Proposée par Answiki le 27/09/2022 à 17:54:54 UTC

Exemples de polynômes du second degré dont les racines sont des nombres entiers ?

Answer   Submitted by Answiki on 09/27/2022 at 05:54:34 PM UTC

Vous trouverez ci-dessous une liste de polynôme du second degré dont les racines sont entières :


Discriminant positif (deux racines distinctes)


  • -5x² - 5x = 0 ===> x1 = 0, x2 = -1
  • -5x² + 5 = 0 ===> x1 = 1, x2 = -1
  • -5x² + 5x = 0 ===> x1 = 1, x2 = 0
  • -4x² - 4x= 0 ===> x1 = 0, x2 = -1
  • -4x² + 4 = 0 ===> x1 = 1, x2 = -1
  • -4x² + 4x = 0 ===> x1 = 1, x2 = 0
  • -3x² - 3x = 0 ===> x1 = 0, x2 = -1
  • -3x² + 3 = 0 ===> x1 = 1, x2 = -1
  • -3x² + 3x = 0 ===> x1 = 1, x2 = 0
  • -2x² - 4x = 0 ===> x1 = 0, x2 = -2
  • -2x² - 2x = 0 ===> x1 = 0, x2 = -1
  • -2x² - 2x+4 = 0 ===> x1 = 1, x2 = -2
  • -2x² +2 = 0 ===> x1 = 1, x2 = -1
  • -2x² + 2x = 0 ===> x1 = 1, x2 = 0
  • -2x² +2x +4 = 0 ===> x1 = 2, x2 = -1
  • -2x² + 4x = 0 ===> x1 = 2, x2 = 0
  • -x² - 5x - 4 = 0 ===> x1 = -1, x2 = -4
  • -x² - 5x = 0 ===> x1 = 0, x2 = -5
  • -x² - 4x - 3 = 0 ===> x1 = -1, x2 = -3
  • -x² - 4x = 0 ===> x1 = 0, x2 = -4
  • -x² - 4x + 5 = 0 ===> x1 = 1, x2 = -5
  • -x² - 3x - 2 = 0 ===> x1 = -1, x2 = -2
  • -x² - 3x = 0 ===> x1 = 0, x2 = -3
  • -x² - 3x + 4 = 0 ===> x1 = 1, x2 = -4
  • -x² - 2x = 0 ===> x1 = 0, x2 = -2
  • -x² - 2x + 3 = 0 ===> x1 = 1, x2 = -3
  • -x² - 1x = 0 ===> x1 = 0, x2 = -1
  • -x² - 1x + 2 = 0 ===> x1 = 1, x2 = -2
  • -x² +1 = 0 ===> x1 = 1, x2 = -1
  • -x² +4 = 0 ===> x1 = 2, x2 = -2
  • -x² +1x = 0 ===> x1 = 1, x2 = 0
  • -x² +1x +2 = 0 ===> x1 = 2, x2 = -1
  • -x² + 2x = 0 ===> x1 = 2, x2 = 0
  • -x² + 2x +3 = 0 ===> x1 = 3, x2 = -1
  • -x² + 3x -2 = 0 ===> x1 = 2, x2 = 1
  • -x² + 3x = 0 ===> x1 = 3, x2 = 0
  • -x² + 3x +4 = 0 ===> x1 = 4, x2 = -1
  • -x² + 4x -3 = 0 ===> x1 = 3, x2 = 1
  • -x² + 4x = 0 ===> x1 = 4, x2 = 0
  • -x² + 4x +5 = 0 ===> x1 = 5, x2 = -1
  • -x² + 5x -4 = 0 ===> x1 = 4, x2 = 1
  • -x² + 5x = 0 ===> x1 = 5, x2 = 0
  • x² - 5x = 0 ===> x1 = 0, x2 = 5
  • x² -5x+4 = 0 ===> x1 = 1, x2 = 4
  • x² -4x-5 = 0 ===> x1 = -1, x2 = 5
  • x² -4x+0 = 0 ===> x1 = 0, x2 = 4
  • x² -4x+3 = 0 ===> x1 = 1, x2 = 3
  • x² -3x-4 = 0 ===> x1 = -1, x2 = 4
  • x² -3x+0 = 0 ===> x1 = 0, x2 = 3
  • x² -3x+2 = 0 ===> x1 = 1, x2 = 2
  • x² -2x-3 = 0 ===> x1 = -1, x2 = 3
  • x² -2x+0 = 0 ===> x1 = 0, x2 = 2
  • x² -1x-2 = 0 ===> x1 = -1, x2 = 2
  • x² -1x = 0 ===> x1 = 0, x2 = 1
  • x² - 4 = 0 ===> x1 = -2, x2 = 2
  • x² - 1 = 0 ===> x1 = -1, x2 = 1
  • x² + 1x - 2 = 0 ===> x1 = -2, x2 = 1
  • x² + 1x = 0 ===> x1 = -1, x2 = 0
  • x² + 2x - 3 = 0 ===> x1 = -3, x2 = 1
  • x² + 2x = 0 ===> x1 = -2, x2 = 0
  • x² + 3x - 4 = 0 ===> x1 = -4, x2 = 1
  • x² + 3x = 0 ===> x1 = -3, x2 = 0
  • x² + 3x + 2 = 0 ===> x1 = -2, x2 = -1
  • x² + 4x - 5 = 0 ===> x1 = -5, x2 = 1
  • x² + 4x = 0 ===> x1 = -4, x2 = 0
  • x² + 4x + 3 = 0 ===> x1 = -3, x2 = -1
  • x² + 5x = 0 ===> x1 = -5, x2 = 0
  • x² + 5x + 4 = 0 ===> x1 = -4, x2 = -1
  • 2x² - 4x = 0 ===> x1 = 0, x2 = 2
  • 2x² - 2x - 4 = 0 ===> x1 = -1, x2 = 2
  • 2x² -2x + 0 = 0 ===> x1 = 0, x2 = 1
  • 2x² +0x - 2 = 0 ===> x1 = -1, x2 = 1
  • 2x² +2x - 4 = 0 ===> x1 = -2, x2 = 1
  • 2x² +2x = 0 ===> x1 = -1, x2 = 0
  • 2x² +4x = 0 ===> x1 = -2, x2 = 0
  • 3x² - 3x = 0 ===> x1 = 0, x2 = 1
  • 3x² - 3 = 0 ===> x1 = -1, x2 = 1
  • 3x² + 3x = 0 ===> x1 = -1, x2 = 0
  • 4x² - 4x = 0 ===> x1 = 0, x2 = 1
  • 4x² - 4 = 0 ===> x1 = -1, x2 = 1
  • 4x² +4x = 0 ===> x1 = -1, x2 = 0
  • 5x² - 5x = 0 ===> x1 = 0, x2 = 1
  • 5x² - 5 = 0 ===> x1 = -1, x2 = 1
  • 5x² +5x = 0 ===> x1 = -1, x2 = 0


Discriminant nul (deux racines identiques)


  • -8x² = 0 ===> x1 = x2 = 0
  • -7x² = 0 ===> x1 = x2 = 0
  • -6x² = 0 ===> x1 = x2 = 0
  • -5x² = 0 ===> x1 = x2 = 0
  • -4x² - 8x - 4 = 0 ===> x1 = x2 = -1
  • -4x² = 0 ===> x1 = x2 = 0
  • -4x² + 8x - 4 = 0 ===> x1 = x2 = 1
  • -3x² - 6x - 3 = 0 ===> x1 = x2 = -1
  • -3x² = 0 ===> x1 = x2 = 0
  • -3x² + 6x - 3 = 0 ===> x1 = x2 = 1
  • -2x² - 8x - 8 = 0 ===> x1 = x2 = -2
  • -2x² - 4x - 2 = 0 ===> x1 = x2 = -1
  • -2x² = 0 ===> x1 = x2 = 0
  • -2x² + 4x - 2 = 0 ===> x1 = x2 = 1
  • -2x² + 8x - 8 = 0 ===> x1 = x2 = 2
  • -x² - 4x - 4 = 0 ===> x1 = x2 = -2
  • -x² - 2x - 1 = 0 ===> x1 = x2 = -1
  • -x² = 0 ===> x1 = x2 = 0
  • -x² + 2x - 1 = 0 ===> x1 = x2 = 1
  • -x² + 4x - 4 = 0 ===> x1 = x2 = 2
  • x² - 4x + 4 = 0 ===> x1 = x2 = 2
  • x² - 2x + 1 = 0 ===> x1 = x2 = 1
  • x² = 0 ===> x1 = x2 = 0
  • x² + 2x + 1 = 0 ===> x1 = x2 = -1
  • x² + 4x + 4 = 0 ===> x1 = x2 = -2
  • 2x² - 8x + 8 = 0 ===> x1 = x2 = 2
  • 2x² - 4x + 2 = 0 ===> x1 = x2 = 1
  • 2x² = 0 ===> x1 = x2 = 0
  • 2x² + 4x + 2 = 0 ===> x1 = x2 = -1
  • 2x² + 8x + 8 = 0 ===> x1 = x2 = -2
  • 3x² - 6x + 3 = 0 ===> x1 = x2 = 1
  • 3x² = 0 ===> x1 = x2 = 0
  • 3x² + 6x + 3 = 0 ===> x1 = x2 = -1
  • 4x² - 8x + 4 = 0 ===> x1 = x2 = 1
  • 4x² = 0 ===> x1 = x2 = 0
  • 4x² + 8x + 4 = 0 ===> x1 = x2 = -1
  • 5x² = 0 ===> x1 = x2 = 0
  • 6x² = 0 ===> x1 = x2 = 0
  • 7x² = 0 ===> x1 = x2 = 0
  • 8x² = 0 ===> x1 = x2 = 0
5 events in history
Question by Answiki 09/27/2022 at 05:54:54 PM
Exemples de polynômes du second degré dont les racines sont des nombres entiers ?
Answer by Answiki on 09/27/2022 at 05:54:34 PM

Vous trouverez ci-dessous une liste de polynôme du second degré dont les racines sont entières :


Discriminant positif (deux racines distinctes)


  • -5x² - 5x = 0 ===> x1 = 0, x2 = -1
  • -5x² + 5 = 0 ===> x1 = 1, x2 = -1
  • -5x² + 5x = 0 ===> x1 = 1, x2 = 0
  • -4x² - 4x= 0 ===> x1 = 0, x2 = -1
  • -4x² + 4 = 0 ===> x1 = 1, x2 = -1
  • -4x² + 4x = 0 ===> x1 = 1, x2 = 0
  • -3x² - 3x = 0 ===> x1 = 0, x2 = -1
  • -3x² + 3 = 0 ===> x1 = 1, x2 = -1
  • -3x² + 3x = 0 ===> x1 = 1, x2 = 0
  • -2x² - 4x = 0 ===> x1 = 0, x2 = -2
  • -2x² - 2x = 0 ===> x1 = 0, x2 = -1
  • -2x² - 2x+4 = 0 ===> x1 = 1, x2 = -2
  • -2x² +2 = 0 ===> x1 = 1, x2 = -1
  • -2x² + 2x = 0 ===> x1 = 1, x2 = 0
  • -2x² +2x +4 = 0 ===> x1 = 2, x2 = -1
  • -2x² + 4x = 0 ===> x1 = 2, x2 = 0
  • -x² - 5x - 4 = 0 ===> x1 = -1, x2 = -4
  • -x² - 5x = 0 ===> x1 = 0, x2 = -5
  • -x² - 4x - 3 = 0 ===> x1 = -1, x2 = -3
  • -x² - 4x = 0 ===> x1 = 0, x2 = -4
  • -x² - 4x + 5 = 0 ===> x1 = 1, x2 = -5
  • -x² - 3x - 2 = 0 ===> x1 = -1, x2 = -2
  • -x² - 3x = 0 ===> x1 = 0, x2 = -3
  • -x² - 3x + 4 = 0 ===> x1 = 1, x2 = -4
  • -x² - 2x = 0 ===> x1 = 0, x2 = -2
  • -x² - 2x + 3 = 0 ===> x1 = 1, x2 = -3
  • -x² - 1x = 0 ===> x1 = 0, x2 = -1
  • -x² - 1x + 2 = 0 ===> x1 = 1, x2 = -2
  • -x² +1 = 0 ===> x1 = 1, x2 = -1
  • -x² +4 = 0 ===> x1 = 2, x2 = -2
  • -x² +1x = 0 ===> x1 = 1, x2 = 0
  • -x² +1x +2 = 0 ===> x1 = 2, x2 = -1
  • -x² + 2x = 0 ===> x1 = 2, x2 = 0
  • -x² + 2x +3 = 0 ===> x1 = 3, x2 = -1
  • -x² + 3x -2 = 0 ===> x1 = 2, x2 = 1
  • -x² + 3x = 0 ===> x1 = 3, x2 = 0
  • -x² + 3x +4 = 0 ===> x1 = 4, x2 = -1
  • -x² + 4x -3 = 0 ===> x1 = 3, x2 = 1
  • -x² + 4x = 0 ===> x1 = 4, x2 = 0
  • -x² + 4x +5 = 0 ===> x1 = 5, x2 = -1
  • -x² + 5x -4 = 0 ===> x1 = 4, x2 = 1
  • -x² + 5x = 0 ===> x1 = 5, x2 = 0
  • x² - 5x = 0 ===> x1 = 0, x2 = 5
  • x² -5x+4 = 0 ===> x1 = 1, x2 = 4
  • x² -4x-5 = 0 ===> x1 = -1, x2 = 5
  • x² -4x+0 = 0 ===> x1 = 0, x2 = 4
  • x² -4x+3 = 0 ===> x1 = 1, x2 = 3
  • x² -3x-4 = 0 ===> x1 = -1, x2 = 4
  • x² -3x+0 = 0 ===> x1 = 0, x2 = 3
  • x² -3x+2 = 0 ===> x1 = 1, x2 = 2
  • x² -2x-3 = 0 ===> x1 = -1, x2 = 3
  • x² -2x+0 = 0 ===> x1 = 0, x2 = 2
  • x² -1x-2 = 0 ===> x1 = -1, x2 = 2
  • x² -1x = 0 ===> x1 = 0, x2 = 1
  • x² - 4 = 0 ===> x1 = -2, x2 = 2
  • x² - 1 = 0 ===> x1 = -1, x2 = 1
  • x² + 1x - 2 = 0 ===> x1 = -2, x2 = 1
  • x² + 1x = 0 ===> x1 = -1, x2 = 0
  • x² + 2x - 3 = 0 ===> x1 = -3, x2 = 1
  • x² + 2x = 0 ===> x1 = -2, x2 = 0
  • x² + 3x - 4 = 0 ===> x1 = -4, x2 = 1
  • x² + 3x = 0 ===> x1 = -3, x2 = 0
  • x² + 3x + 2 = 0 ===> x1 = -2, x2 = -1
  • x² + 4x - 5 = 0 ===> x1 = -5, x2 = 1
  • x² + 4x = 0 ===> x1 = -4, x2 = 0
  • x² + 4x + 3 = 0 ===> x1 = -3, x2 = -1
  • x² + 5x = 0 ===> x1 = -5, x2 = 0
  • x² + 5x + 4 = 0 ===> x1 = -4, x2 = -1
  • 2x² - 4x = 0 ===> x1 = 0, x2 = 2
  • 2x² - 2x - 4 = 0 ===> x1 = -1, x2 = 2
  • 2x² -2x + 0 = 0 ===> x1 = 0, x2 = 1
  • 2x² +0x - 2 = 0 ===> x1 = -1, x2 = 1
  • 2x² +2x - 4 = 0 ===> x1 = -2, x2 = 1
  • 2x² +2x = 0 ===> x1 = -1, x2 = 0
  • 2x² +4x = 0 ===> x1 = -2, x2 = 0
  • 3x² - 3x = 0 ===> x1 = 0, x2 = 1
  • 3x² - 3 = 0 ===> x1 = -1, x2 = 1
  • 3x² + 3x = 0 ===> x1 = -1, x2 = 0
  • 4x² - 4x = 0 ===> x1 = 0, x2 = 1
  • 4x² - 4 = 0 ===> x1 = -1, x2 = 1
  • 4x² +4x = 0 ===> x1 = -1, x2 = 0
  • 5x² - 5x = 0 ===> x1 = 0, x2 = 1
  • 5x² - 5 = 0 ===> x1 = -1, x2 = 1
  • 5x² +5x = 0 ===> x1 = -1, x2 = 0


Discriminant nul (deux racines identiques)


  • -8x² = 0 ===> x1 = x2 = 0
  • -7x² = 0 ===> x1 = x2 = 0
  • -6x² = 0 ===> x1 = x2 = 0
  • -5x² = 0 ===> x1 = x2 = 0
  • -4x² - 8x - 4 = 0 ===> x1 = x2 = -1
  • -4x² = 0 ===> x1 = x2 = 0
  • -4x² + 8x - 4 = 0 ===> x1 = x2 = 1
  • -3x² - 6x - 3 = 0 ===> x1 = x2 = -1
  • -3x² = 0 ===> x1 = x2 = 0
  • -3x² + 6x - 3 = 0 ===> x1 = x2 = 1
  • -2x² - 8x - 8 = 0 ===> x1 = x2 = -2
  • -2x² - 4x - 2 = 0 ===> x1 = x2 = -1
  • -2x² = 0 ===> x1 = x2 = 0
  • -2x² + 4x - 2 = 0 ===> x1 = x2 = 1
  • -2x² + 8x - 8 = 0 ===> x1 = x2 = 2
  • -x² - 4x - 4 = 0 ===> x1 = x2 = -2
  • -x² - 2x - 1 = 0 ===> x1 = x2 = -1
  • -x² = 0 ===> x1 = x2 = 0
  • -x² + 2x - 1 = 0 ===> x1 = x2 = 1
  • -x² + 4x - 4 = 0 ===> x1 = x2 = 2
  • x² - 4x + 4 = 0 ===> x1 = x2 = 2
  • x² - 2x + 1 = 0 ===> x1 = x2 = 1
  • x² = 0 ===> x1 = x2 = 0
  • x² + 2x + 1 = 0 ===> x1 = x2 = -1
  • x² + 4x + 4 = 0 ===> x1 = x2 = -2
  • 2x² - 8x + 8 = 0 ===> x1 = x2 = 2
  • 2x² - 4x + 2 = 0 ===> x1 = x2 = 1
  • 2x² = 0 ===> x1 = x2 = 0
  • 2x² + 4x + 2 = 0 ===> x1 = x2 = -1
  • 2x² + 8x + 8 = 0 ===> x1 = x2 = -2
  • 3x² - 6x + 3 = 0 ===> x1 = x2 = 1
  • 3x² = 0 ===> x1 = x2 = 0
  • 3x² + 6x + 3 = 0 ===> x1 = x2 = -1
  • 4x² - 8x + 4 = 0 ===> x1 = x2 = 1
  • 4x² = 0 ===> x1 = x2 = 0
  • 4x² + 8x + 4 = 0 ===> x1 = x2 = -1
  • 5x² = 0 ===> x1 = x2 = 0
  • 6x² = 0 ===> x1 = x2 = 0
  • 7x² = 0 ===> x1 = x2 = 0
  • 8x² = 0 ===> x1 = x2 = 0
Answer by Answiki on 09/27/2022 at 05:47:50 PM

Vous trouverez ci-dessous une liste de polynôme du second degré dont les racines sont entières :


Discriminant positif (deux racines distinctes)


  • -5x² -5x+0 = 0 ===> x1 = 0, x2 = -1
  • -5x² +0x +5 = 0 ===> x1 = 1, x2 = -1
  • -5x² +5x +0 = 0 ===> x1 = 1, x2 = 0
  • -4x² -4x+0 = 0 ===> x1 = 0, x2 = -1
  • -4x² +0x +4 = 0 ===> x1 = 1, x2 = -1
  • -4x² +4x +0 = 0 ===> x1 = 1, x2 = 0
  • -3x² -3x+0 = 0 ===> x1 = 0, x2 = -1
  • -3x² +0x +3 = 0 ===> x1 = 1, x2 = -1
  • -3x² +3x +0 = 0 ===> x1 = 1, x2 = 0
  • -2x² -4x+0 = 0 ===> x1 = 0, x2 = -2
  • -2x² -2x+0 = 0 ===> x1 = 0, x2 = -1
  • -2x² -2x+4 = 0 ===> x1 = 1, x2 = -2
  • -2x² +0x +2 = 0 ===> x1 = 1, x2 = -1
  • -2x² +2x +0 = 0 ===> x1 = 1, x2 = 0
  • -2x² +2x +4 = 0 ===> x1 = 2, x2 = -1
  • -2x² +4x +0 = 0 ===> x1 = 2, x2 = 0
  • -1x² -5x-4 = 0 ===> x1 = -1, x2 = -4
  • -1x² -5x+0 = 0 ===> x1 = 0, x2 = -5
  • -1x² -4x-3 = 0 ===> x1 = -1, x2 = -3
  • -1x² -4x+0 = 0 ===> x1 = 0, x2 = -4
  • -1x² -4x+5 = 0 ===> x1 = 1, x2 = -5
  • -1x² -3x-2 = 0 ===> x1 = -1, x2 = -2
  • -1x² -3x+0 = 0 ===> x1 = 0, x2 = -3
  • -1x² -3x+4 = 0 ===> x1 = 1, x2 = -4
  • -1x² -2x+0 = 0 ===> x1 = 0, x2 = -2
  • -1x² -2x+3 = 0 ===> x1 = 1, x2 = -3
  • -1x² -1x+0 = 0 ===> x1 = 0, x2 = -1
  • -1x² -1x+2 = 0 ===> x1 = 1, x2 = -2
  • -1x² +0x +1 = 0 ===> x1 = 1, x2 = -1
  • -1x² +0x +4 = 0 ===> x1 = 2, x2 = -2
  • -1x² +1x +0 = 0 ===> x1 = 1, x2 = 0
  • -1x² +1x +2 = 0 ===> x1 = 2, x2 = -1
  • -1x² +2x +0 = 0 ===> x1 = 2, x2 = 0
  • -1x² +2x +3 = 0 ===> x1 = 3, x2 = -1
  • -1x² +3x -2 = 0 ===> x1 = 2, x2 = 1
  • -1x² +3x +0 = 0 ===> x1 = 3, x2 = 0
  • -1x² +3x +4 = 0 ===> x1 = 4, x2 = -1
  • -1x² +4x -3 = 0 ===> x1 = 3, x2 = 1
  • -1x² +4x +0 = 0 ===> x1 = 4, x2 = 0
  • -1x² +4x +5 = 0 ===> x1 = 5, x2 = -1
  • -1x² +5x -4 = 0 ===> x1 = 4, x2 = 1
  • -1x² +5x +0 = 0 ===> x1 = 5, x2 = 0
  • 1x² -5x+0 = 0 ===> x1 = 0, x2 = 5
  • 1x² -5x+4 = 0 ===> x1 = 1, x2 = 4
  • 1x² -4x-5 = 0 ===> x1 = -1, x2 = 5
  • 1x² -4x+0 = 0 ===> x1 = 0, x2 = 4
  • 1x² -4x+3 = 0 ===> x1 = 1, x2 = 3
  • 1x² -3x-4 = 0 ===> x1 = -1, x2 = 4
  • 1x² -3x+0 = 0 ===> x1 = 0, x2 = 3
  • 1x² -3x+2 = 0 ===> x1 = 1, x2 = 2
  • 1x² -2x-3 = 0 ===> x1 = -1, x2 = 3
  • 1x² -2x+0 = 0 ===> x1 = 0, x2 = 2
  • 1x² -1x-2 = 0 ===> x1 = -1, x2 = 2
  • 1x² -1x+0 = 0 ===> x1 = 0, x2 = 1
  • 1x² +0x -4 = 0 ===> x1 = -2, x2 = 2
  • 1x² +0x -1 = 0 ===> x1 = -1, x2 = 1
  • 1x² +1x -2 = 0 ===> x1 = -2, x2 = 1
  • 1x² +1x +0 = 0 ===> x1 = -1, x2 = 0
  • 1x² +2x -3 = 0 ===> x1 = -3, x2 = 1
  • 1x² +2x +0 = 0 ===> x1 = -2, x2 = 0
  • 1x² +3x -4 = 0 ===> x1 = -4, x2 = 1
  • 1x² +3x +0 = 0 ===> x1 = -3, x2 = 0
  • 1x² +3x +2 = 0 ===> x1 = -2, x2 = -1
  • 1x² +4x -5 = 0 ===> x1 = -5, x2 = 1
  • 1x² +4x +0 = 0 ===> x1 = -4, x2 = 0
  • 1x² +4x +3 = 0 ===> x1 = -3, x2 = -1
  • 1x² +5x +0 = 0 ===> x1 = -5, x2 = 0
  • 1x² +5x +4 = 0 ===> x1 = -4, x2 = -1
  • 2x² -4x+0 = 0 ===> x1 = 0, x2 = 2
  • 2x² -2x-4 = 0 ===> x1 = -1, x2 = 2
  • 2x² -2x+0 = 0 ===> x1 = 0, x2 = 1
  • 2x² +0x -2 = 0 ===> x1 = -1, x2 = 1
  • 2x² +2x -4 = 0 ===> x1 = -2, x2 = 1
  • 2x² +2x +0 = 0 ===> x1 = -1, x2 = 0
  • 2x² +4x +0 = 0 ===> x1 = -2, x2 = 0
  • 3x² -3x+0 = 0 ===> x1 = 0, x2 = 1
  • 3x² +0x -3 = 0 ===> x1 = -1, x2 = 1
  • 3x² +3x +0 = 0 ===> x1 = -1, x2 = 0
  • 4x² -4x+0 = 0 ===> x1 = 0, x2 = 1
  • 4x² +0x -4 = 0 ===> x1 = -1, x2 = 1
  • 4x² +4x +0 = 0 ===> x1 = -1, x2 = 0
  • 5x² -5x+0 = 0 ===> x1 = 0, x2 = 1
  • 5x² +0x -5 = 0 ===> x1 = -1, x2 = 1
  • 5x² +5x +0 = 0 ===> x1 = -1, x2 = 0


Discriminant nul (deux racines identiques)


  • -8x² +0x +0 = 0 ===> x1 = x2 = 0
  • -7x² +0x +0 = 0 ===> x1 = x2 = 0
  • -6x² +0x +0 = 0 ===> x1 = x2 = 0
  • -5x² +0x +0 = 0 ===> x1 = x2 = 0
  • -4x² -8x-4 = 0 ===> x1 = x2 = -1
  • -4x² +0x +0 = 0 ===> x1 = x2 = 0
  • -4x² +8x -4 = 0 ===> x1 = x2 = 1
  • -3x² -6x-3 = 0 ===> x1 = x2 = -1
  • -3x² +0x +0 = 0 ===> x1 = x2 = 0
  • -3x² +6x -3 = 0 ===> x1 = x2 = 1
  • -2x² -8x-8 = 0 ===> x1 = x2 = -2
  • -2x² -4x-2 = 0 ===> x1 = x2 = -1
  • -2x² +0x +0 = 0 ===> x1 = x2 = 0
  • -2x² +4x -2 = 0 ===> x1 = x2 = 1
  • -2x² +8x -8 = 0 ===> x1 = x2 = 2
  • -1x² -4x-4 = 0 ===> x1 = x2 = -2
  • -1x² -2x-1 = 0 ===> x1 = x2 = -1
  • -1x² +0x +0 = 0 ===> x1 = x2 = 0
  • -1x² +2x -1 = 0 ===> x1 = x2 = 1
  • -1x² +4x -4 = 0 ===> x1 = x2 = 2
  • 1x² -4x+4 = 0 ===> x1 = x2 = 2
  • 1x² -2x+1 = 0 ===> x1 = x2 = 1
  • 1x² +0x +0 = 0 ===> x1 = x2 = 0
  • 1x² +2x +1 = 0 ===> x1 = x2 = -1
  • 1x² +4x +4 = 0 ===> x1 = x2 = -2
  • 2x² -8x+8 = 0 ===> x1 = x2 = 2
  • 2x² -4x+2 = 0 ===> x1 = x2 = 1
  • 2x² +0x +0 = 0 ===> x1 = x2 = 0
  • 2x² +4x +2 = 0 ===> x1 = x2 = -1
  • 2x² +8x +8 = 0 ===> x1 = x2 = -2
  • 3x² -6x+3 = 0 ===> x1 = x2 = 1
  • 3x² +0x +0 = 0 ===> x1 = x2 = 0
  • 3x² +6x +3 = 0 ===> x1 = x2 = -1
  • 4x² -8x+4 = 0 ===> x1 = x2 = 1
  • 4x² +0x +0 = 0 ===> x1 = x2 = 0
  • 4x² +8x +4 = 0 ===> x1 = x2 = -1
  • 5x² +0x +0 = 0 ===> x1 = x2 = 0
  • 6x² +0x +0 = 0 ===> x1 = x2 = 0
  • 7x² +0x +0 = 0 ===> x1 = x2 = 0
  • 8x² +0x +0 = 0 ===> x1 = x2 = 0
Answer by Answiki on 09/27/2022 at 05:43:11 PM

Vous trouverez ci-dessous une liste de polynôme du second degré dont les racines sont entières :


Discriminant positif (deux racines distinctes)


  • -5x² -5x+0 = 0 ===> x1 = 0, x2 = -1
  • -5x² +0x +5 = 0 ===> x1 = 1, x2 = -1
  • -5x² +5x +0 = 0 ===> x1 = 1, x2 = 0
  • -4x² -4x+0 = 0 ===> x1 = 0, x2 = -1
  • -4x² +0x +4 = 0 ===> x1 = 1, x2 = -1
  • -4x² +4x +0 = 0 ===> x1 = 1, x2 = 0
  • -3x² -3x+0 = 0 ===> x1 = 0, x2 = -1
  • -3x² +0x +3 = 0 ===> x1 = 1, x2 = -1
  • -3x² +3x +0 = 0 ===> x1 = 1, x2 = 0
  • -2x² -4x+0 = 0 ===> x1 = 0, x2 = -2
  • -2x² -2x+0 = 0 ===> x1 = 0, x2 = -1
  • -2x² -2x+4 = 0 ===> x1 = 1, x2 = -2
  • -2x² +0x +2 = 0 ===> x1 = 1, x2 = -1
  • -2x² +2x +0 = 0 ===> x1 = 1, x2 = 0
  • -2x² +2x +4 = 0 ===> x1 = 2, x2 = -1
  • -2x² +4x +0 = 0 ===> x1 = 2, x2 = 0
  • -1x² -5x-4 = 0 ===> x1 = -1, x2 = -4
  • -1x² -5x+0 = 0 ===> x1 = 0, x2 = -5
  • -1x² -4x-3 = 0 ===> x1 = -1, x2 = -3
  • -1x² -4x+0 = 0 ===> x1 = 0, x2 = -4
  • -1x² -4x+5 = 0 ===> x1 = 1, x2 = -5
  • -1x² -3x-2 = 0 ===> x1 = -1, x2 = -2
  • -1x² -3x+0 = 0 ===> x1 = 0, x2 = -3
  • -1x² -3x+4 = 0 ===> x1 = 1, x2 = -4
  • -1x² -2x+0 = 0 ===> x1 = 0, x2 = -2
  • -1x² -2x+3 = 0 ===> x1 = 1, x2 = -3
  • -1x² -1x+0 = 0 ===> x1 = 0, x2 = -1
  • -1x² -1x+2 = 0 ===> x1 = 1, x2 = -2
  • -1x² +0x +1 = 0 ===> x1 = 1, x2 = -1
  • -1x² +0x +4 = 0 ===> x1 = 2, x2 = -2
  • -1x² +1x +0 = 0 ===> x1 = 1, x2 = 0
  • -1x² +1x +2 = 0 ===> x1 = 2, x2 = -1
  • -1x² +2x +0 = 0 ===> x1 = 2, x2 = 0
  • -1x² +2x +3 = 0 ===> x1 = 3, x2 = -1
  • -1x² +3x -2 = 0 ===> x1 = 2, x2 = 1
  • -1x² +3x +0 = 0 ===> x1 = 3, x2 = 0
  • -1x² +3x +4 = 0 ===> x1 = 4, x2 = -1
  • -1x² +4x -3 = 0 ===> x1 = 3, x2 = 1
  • -1x² +4x +0 = 0 ===> x1 = 4, x2 = 0
  • -1x² +4x +5 = 0 ===> x1 = 5, x2 = -1
  • -1x² +5x -4 = 0 ===> x1 = 4, x2 = 1
  • -1x² +5x +0 = 0 ===> x1 = 5, x2 = 0
  • 1x² -5x+0 = 0 ===> x1 = 0, x2 = 5
  • 1x² -5x+4 = 0 ===> x1 = 1, x2 = 4
  • 1x² -4x-5 = 0 ===> x1 = -1, x2 = 5
  • 1x² -4x+0 = 0 ===> x1 = 0, x2 = 4
  • 1x² -4x+3 = 0 ===> x1 = 1, x2 = 3
  • 1x² -3x-4 = 0 ===> x1 = -1, x2 = 4
  • 1x² -3x+0 = 0 ===> x1 = 0, x2 = 3
  • 1x² -3x+2 = 0 ===> x1 = 1, x2 = 2
  • 1x² -2x-3 = 0 ===> x1 = -1, x2 = 3
  • 1x² -2x+0 = 0 ===> x1 = 0, x2 = 2
  • 1x² -1x-2 = 0 ===> x1 = -1, x2 = 2
  • 1x² -1x+0 = 0 ===> x1 = 0, x2 = 1
  • 1x² +0x -4 = 0 ===> x1 = -2, x2 = 2
  • 1x² +0x -1 = 0 ===> x1 = -1, x2 = 1
  • 1x² +1x -2 = 0 ===> x1 = -2, x2 = 1
  • 1x² +1x +0 = 0 ===> x1 = -1, x2 = 0
  • 1x² +2x -3 = 0 ===> x1 = -3, x2 = 1
  • 1x² +2x +0 = 0 ===> x1 = -2, x2 = 0
  • 1x² +3x -4 = 0 ===> x1 = -4, x2 = 1
  • 1x² +3x +0 = 0 ===> x1 = -3, x2 = 0
  • 1x² +3x +2 = 0 ===> x1 = -2, x2 = -1
  • 1x² +4x -5 = 0 ===> x1 = -5, x2 = 1
  • 1x² +4x +0 = 0 ===> x1 = -4, x2 = 0
  • 1x² +4x +3 = 0 ===> x1 = -3, x2 = -1
  • 1x² +5x +0 = 0 ===> x1 = -5, x2 = 0
  • 1x² +5x +4 = 0 ===> x1 = -4, x2 = -1
  • 2x² -4x+0 = 0 ===> x1 = 0, x2 = 2
  • 2x² -2x-4 = 0 ===> x1 = -1, x2 = 2
  • 2x² -2x+0 = 0 ===> x1 = 0, x2 = 1
  • 2x² +0x -2 = 0 ===> x1 = -1, x2 = 1
  • 2x² +2x -4 = 0 ===> x1 = -2, x2 = 1
  • 2x² +2x +0 = 0 ===> x1 = -1, x2 = 0
  • 2x² +4x +0 = 0 ===> x1 = -2, x2 = 0
  • 3x² -3x+0 = 0 ===> x1 = 0, x2 = 1
  • 3x² +0x -3 = 0 ===> x1 = -1, x2 = 1
  • 3x² +3x +0 = 0 ===> x1 = -1, x2 = 0
  • 4x² -4x+0 = 0 ===> x1 = 0, x2 = 1
  • 4x² +0x -4 = 0 ===> x1 = -1, x2 = 1
  • 4x² +4x +0 = 0 ===> x1 = -1, x2 = 0
  • 5x² -5x+0 = 0 ===> x1 = 0, x2 = 1
  • 5x² +0x -5 = 0 ===> x1 = -1, x2 = 1
  • 5x² +5x +0 = 0 ===> x1 = -1, x2 = 0
Question by Answiki 09/26/2022 at 09:15:53 PM
Exemples de polynômes du second degré qui tombent juste ?
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