Bonjour,
f(x)= 4(x-1.5)²-4
f(x)= 4(x²-1.5x-1.5x+2.25)-4
f(x)= 4x²-12x+9-4
f(x)= 4x²-12x+5
f(x)= (2x-5)(2x-1)
f(x)= 4x²-10x-2x+5
f(x)= 4x²-12x+5
Donc 4(x-1.5)²-4 = (2x-5)(2x-1)
Résoudre f(x)=-4
4x²-12x+5=-4
4x²-12x+5+4=0
4x²-12x+9=0
Δ = 0
Δ = 0 ; solution double xo= -b/2a=12/8= 3/2
4(x − 3/2)²=0
x=3/2
f(x)≥ 5
4x²-12x+5 ≥ 5
4x²-12x+5-5 ≥ 0
4x²-12x ≥ 0
4x(x-3) ≥ 0
x=0
x=3
S= ] -∞; 0]∪[3; +∞[
4x²-12x+5=0
Δ = 64
x1= 1/2 et x2= 5/2
