Bonjour,
f(x)= x-3+3(x-3)²+x²-9
Développer et réduire f(x)
f(x)= x-3+3(x²-3x-3x+9)+x²-9
f(x)= x-3+3x²-18x+27+x²-9
f(x)= 4x²-17x+15
Factoriser f(x)
f(x)= x-3+3(x-3)²+x²-9
f(x)= x-3+3(x-3)²+x²-9
f(x)= (x-3)+3(x-3)(x-3)+(x-3)(x+3)
f(x)= (x-3)(1+3(x-3)+x+3)
f(x)= (x-3)(1+3x-9+x+3)
f(x)= (x-3)(4x-5)
Calcul de:
f(x0)= 4(0)²-17(0)+15= 15
f(5/4)= 4(5/4)²-17(5/4)+15= 100/16-85/4+15=(100-85*4+15*16)/16
= 1200/16= 75
Résoudre :
. f(x)= 0
(x-3)(4x-5)= 0
x= 3 ou x= 5/4 S={ 5/4 ; 3 }
. f(x)= 15
4x²-17x+15= 15
4x²-17x+15-15= 0
4x²-17x= 0
x(4x-17)= 0
x= 0 ou x= 17/4 S= { 0 ; 17/4 }
. f(x) ≥ 0
(x-3)(4x-5) ≥ 0
x= 3 ou x= 5/4
S= ]-∞ ; 5/4 ] U [ 3 ; +∞[
A construire la courbe
