Réponse :
(x) =2x²-4x-6
1) f(x) =2(x-1)²-8 = 2(x²-2x+1)-8 = 2x²-4x+2-8 = 2x²-4x-6
f(x) = 2(x-3)(x+1) developpe et reduis
2) 2(x-3)(x+1)=0
x-3=0⇔x=3
x+1=0⇔-1
b) 2x²-4x-6
2x²-4x-6=-6
2x²-4x-6+6=0
2x²-4x=0
2x(x-2)=0
x=2;0
c) 2x²-4x-6<-6
2x²-4x-6+6<0
2x²-4x<0
Δ=b²-4ac = (-4)²-4(2*0) = 16
Δ>0
(-b-√Δ)/2a= (4-4)/2 =0
(-b+√Δ)/2a=(4+4)/4=2
]0;2[
d) 2x²-4x-6>10
2x²-4x-6+10>0
2x²-4x+4>0
Δ=(-4)²-4(2*4)=16-32=-16
Δ<0 pas de solution dans R
