Soient les fonctions f et g definies sur R par:

f(x)=5x+20-3(2x-1)(x+4) et g(x)=(2x+3)²-(x-1)²

1) Developper et reduire f(x) et g(x) (je l est deja fait)

2) Factoriser f(x) et g(x)

3) Resoudre les equations a) f(x)= 0 b) g(x)=8 c) f(x) = g(x)

1

Réponses

2013-11-28T15:07:04+01:00
F(x)=5x+20-3(2x-1)(x+4)
= 5x+20-3(2x²+8x-x-4) = 5x+20-6x²-24x+3x+12 = -6x²-16x+36

a=-6
b=-16
c=36
delta=b²-4ac = 1120

x1 = (-b+racine(delta))/2a = (16+racine(1120))/-12

x2 = (-b-racine(delta))/2a = (16-racine(1120))/-12

F(x) = a(x-x1)(x-x2) = -6(x-x1)(x-x2)


G(x)=(2x+3)²-(x-1)²

G(x) = (2x+3+x-1) (2x+3-x+1) = (3x+2)(x+4)
G(x) = 3x²+14x+8

delta = 100
racine(delta)=10

x1 = (-b+racine(delta))/2a = (-14+10)/6 = -4/6 = -2/3

x2 = (-b-racine(delta))/2a = (-14-10)/6 = -4

G(x)=8 -> 3x²+14x+8=8 -> 3x²+14x=0
delta=196
x1=0 et x2=-4,667