Réponse :
Explications étape par étape
Bonjour
1) image de (-6), 0 et -5/2 :
f(-6) = (-6 - 1)(-6 + 6) = 0
f(0) = 0^2 + 5 * 0 - 6 = -6
f(-5/2) = (-5/2 + 5/2)^2 - 49/4 = -49/4
2) image de V2, V3 + 1
f(V2) = (V2)^2 + 5 * V2 - 6 = 5V2 - 4
f(V3 + 1) = (V3 + 1 - 1)(V3 + 1 + 6) = V3(V3 + 7) = 3 + 7V3
3) résoudre f(x) = 0
(x - 1)(x + 6) = 0
x - 1 = 0 ou x + 6 = 0
x = 1 ou x = -6
4) résoudre f(x) = -6
x^2 + 5x - 6 = -6
x^2 + 5x = 0
x(x + 5) = 0
x = 0 ou x + 5 = 0
x = 0 ou x = -5
5) résoudre f(x) = 15/4
(x + 5/2)^2 - 49/4 = 15/4
(x + 5/2)^2 - 49/4 - 15/4 = 0
(x + 5/2)^2 - 64/4 = 0
(x + 5/2)^2 - (8/2)^2 = 0
(x + 5/2 - 8/2)(x + 5/2 + 8/2) = 0
(x - 3/2)(x + 13/2) = 0
x - 3/2 = 0 ou x + 13/2 = 0
x = 3/2 ou x = -13/2
