Bonjour,
Développement
E(x) = (3 - 5x)² - 25
E(x) = (-5x + 3)² - 25
E(x) = 25x² - 30x + 9 - 25
E(x) = 25x² - 30x - 16
Factorisation
E(x) = (3 - 5x)² - 25
E(x) = (-5x + 3)² - 5²
E(x) = (-5x + 3 - 5)(-5x + 3 + 5)
E(x) = (-5x - 2)(-5x + 8)
E(x) = -25
(3 - 5x)² - 25 = -25
(-5x + 3)² = 0
-5x + 3 = 0
5x = 3
x = 3/5
E(x) > 0
On pose (-5x - 2)(-5x + 8) = 0
-5x - 2 = 0 ou -5x + 8 = 0
-5x = 2 ou 5x = 8
x = -2/5 ou x = 8/5
tableau de signes :
x.......|-∞..........-2/5...........8/5...........+∞
E(x)..|........+.......0........-.......0......+.........
Donc sur l'intervalle ] - ∞ ; -2/5 [ U ] 8/5 ; + ∞ [