Exercice 4! Aidez svp!

f(x) = x^2 + 6x + 5

Calcul du discriminant :
Delta = 6^2 - 4 * 1 * 5
Delta = 36 - 20
Delta = 16 > 0 donc deux solutions possibles

X1 = (-6 - V16) / 2
X1 = (-6 - 4) / 2
X1 = -10 / 2
X1 = -5

X2 = (-6 + V16) / 2
X2 = (-6 + 4) / 2
X2 = -2 / 2
X2 = -1

Tableau de variation :

X. | -inf. -5. -1. +inf
---------------------------------------------------
x^2+6x+5. |. +. O. - O. +

f(x) est croissante sur : ] -inf ; -5 [ et ] -1 ; +inf [
f(x) est décroissante sur : ] -5 ; -1 [

2) trouver le point de coordonnées :

y = 1/2x - 2
f(x) = (x + 5)(x + 1)

(x + 5)(x + 1) = 1/2x - 2
x^2 + 6x + 5 - 1/2x + 2 = 0
x^2 + 12/2x - 1/2x + 7 = 0
x^2 + 11/2x + 7 = 0

Delta = (11/2)^2 - 4 * 1 * 7
Delta = 121/4 - 28
Delta = 121/4 - 112/4
Delta = 9/4 > 0 donc 2 solutions
V(delta) = V(9/4) = 3/2

X3 = (-11/2 - 3/2) / 2
X3 = (-14/2) /2
X3 = -7/2

X4 = (-11/2 + 3/2) / 2
X4 = (-8/2) / 2
X4 = -4/2
X4 = -2

Les points d'intersection sont :

y = 1/2x - 2
y = 1/2 * (-7/2) - 2
y = -7/4 - 8/4
y = -15/4

(-7/2 ; -15/4)

y = 1/2x - 2
y = 1/2 * (-2) - 2
y = -1 - 2
y = -3

(-2 ; -3)