bonjour
f(x)=
4x²-10x+2
a=4
b= -10
c=
2
delta = b²-4ac
=(-10)²-4×4×2
=68
√Δ=√68=2√17
x1=
(-b-√Δ)
/(2a)
=(5-√17)/4
x2=
(-b+√Δ) /(2a)
=(5+√17)/4
solution
= {(5-√17)/4 ; (5+√17)/4}
2)
forme
factorisée
=
a (x-x1)(x-x2) formule du cours
=4
[x- (5-√17)/4] [x-(5+√17)/4]
=
[ 4x- (5-√17)] [ x- (5+√17)/4]
3)
tableau
de signes
x
-∞ (5-√17)/4
(5+√17)/4 +∞
x-
(5-√17)/4 - + +
x-(5+√17)/4
- - +
f(x) + - +
f(x) ≥ 0 pour x ∈]-∞; (5-√17)/4 ] ∪ [(5+√17)/4 ; +∞[
f(x) ≤ 0 pour x ∈ [(5-√17)/4 ; (5+√17)/4 ]
