Réponses

Meilleure réponse !
2014-09-09T21:01:41+02:00
Bonsoir

f(x) = (x+1) ( 3x-2 ) -5 ( x+1 )²

1) Développons f(x)

f(x) = (x+1) ( 3x-2 ) -5 ( x+1 )²
f(x) = (3x² - 2x + 3x - 2) - 5(x² + 2x + 1)
f(x) = 3x² - 2x + 3x - 2 - 5x² - 10x - 5
f(x) = 3x² - 5x² - 2x + 3x - 10x - 2 - 5
f(x) = -2x² - 9x - 7

Factorisons

f(x) = (x+1) ( 3x-2 ) -5 ( x+1 )²
f(x) = (x+1) (3x-2) - 5(x+1)(x+1)
f(x) = (x+1)[(3x-2) - 5(x+1)]
f(x) = (x+1)(3x - 2 - 5x - 5)

f(x) = (x+1)(-2x-7)

Forme canonique de f(x)

on calcule Δ
Δ = b² - 4ac
Δ = (-9)² - 4(-2)(-7)
Δ = 81 - 56
Δ = 25

formule
a[(x+b/2a)² - Δ/4a²

-2[(x+9/4)² - 25/16]