Bonjour j’aurais besoins d’aide pour l’exo 1. Merci.

Bonjour

Exercice 1

g(x) = x^3 - 7x - 6

1. g(x) = (x - 3) (x + 2) (x + 1)
= (x * x + x * 2 - 3 * x - 3 * 2) (x + 1)
= (x² + 2x - 3x - 6) (x + 1)
= (x² - x - 6) (x + 1)
= x² * x + x² * 1 - x * x - x * 1 - 6 * x - 6 * 1
= x^3 + x² - x² - x - 6x - 6
= x^3 - 7x - 6

2. g(x) = 0
<=> (x - 3) (x + 2) (x + 1) = 0
<=> x - 3 = 0      OU      x + 2 = 0      OU      x + 1 = 0
<=> x = 3      OU      x = -2      OU      x = -1

Donc S = {-2 ; -1 ; 3}

Vérification :
g(3) = (3 - 3) (3 + 2) (3 + 1)
= 0 * 5 * 4
= 0
g(-2) = (-2 - 3) (-2 + 2) (-2 + 1)
= -5 * 0 * (-2)
= 0
g(-1) = (-1 - 3) (-1 + 2) (-1 + 1)
= -4 * 1 * 0
= 0

Voilà j'espère avoir pu t'aider ^^