bonjour j'ai un exo de maths a faire mais je n'y arrive pas merci d'avance

Bonsoir,

Soit f(x) = 2x^2 + 7x - 15
g(x) = x^2 + 10x + 25

1) démontrer :

Delta = 7^2 - 4 * 2 * (-15)
Delta = 49 + 120
Delta = 169
Vdelta = V169 = 13 > 0 donc deux solutions

X1 = (-7 - 13)/(2 * 2) = -20/4 = (-5)
X2 = (-7 + 13)/(2 * 2) = 6/4 = 3/2

f(x) = (x + 5)(x - 3/2)
f(x) = (2x - 3)(5 + x)

2) factoriser g(x) :

g(x) = x^2 + 10x + 25
g(x) = (x)^2 + 2 * x * 5 + 5^2
g(x) = (x + 5)^2

3) résoudre : f(x) << g(x)

(2x - 3)(5 + x) << (x + 5)^2
(2x - 3)(5 + x) - (x + 5)^2 << 0
(5 + x)(2x - 3 - x - 5) << 0
(5 + x)(x - 8) << 0

5 + x = 0 ou x - 8 = 0
x = -5 ou x = 8

x..........|....-inf.............(-5).............8...........+inf
5+x....|..............(-)........O.....(+)...........(+).........
x-8......|.............(-).................(-)......O.....(+)......
Eq......|..............(+).......O......(-).....O.......(.+)......

x € ]-inf;-5] U [8;+inf[