Bonjour
a) 3x²-x-2
calculons delta = b²-4ac
delta = (-1)² - 4(3)(-2) = 1 + 24 = 25
delta = 25 et V(25) = 5
x1 = (1+5) / 6 = 6/6 =1
x1 = 1
x2 = (1-5) / 6 = -4/6 = -2/3
x2 = -2/3
S = {-2/3;1}
b) x²+5=0
x² = -5 impossible car le carré d'un nombre n'est jamais négatif
S = ∅
c) -x²+5x-1 ≤ 0
Calculons delta = b²-4ac
delta = 5² - 4(-1)(-1) = 25 - 4 = 21
delta = 21
x1 = (-5-V21) / -2 = (5+V21) / 2
x2 = (-5 + V21) / -2 = (5-V21) / 2
tableau de signe
x I -oo (5-V21)/2 (5+V21)/2 +oo
-x²+5x-1 - 0 + 0 -
S = ]-oo;(5-V21)/2]U[(5+V21)/2;+oo[
Copyright © 2024 ELIBRARY.TIPS - All rights reserved.
Lista de comentários
Bonjour
a) 3x²-x-2
calculons delta = b²-4ac
delta = (-1)² - 4(3)(-2) = 1 + 24 = 25
delta = 25 et V(25) = 5
x1 = (1+5) / 6 = 6/6 =1
x1 = 1
x2 = (1-5) / 6 = -4/6 = -2/3
x2 = -2/3
S = {-2/3;1}
b) x²+5=0
x² = -5 impossible car le carré d'un nombre n'est jamais négatif
S = ∅
c) -x²+5x-1 ≤ 0
Calculons delta = b²-4ac
delta = 5² - 4(-1)(-1) = 25 - 4 = 21
delta = 21
x1 = (-5-V21) / -2 = (5+V21) / 2
x2 = (-5 + V21) / -2 = (5-V21) / 2
tableau de signe
x I -oo (5-V21)/2 (5+V21)/2 +oo
-x²+5x-1 - 0 + 0 -
S = ]-oo;(5-V21)/2]U[(5+V21)/2;+oo[