Réponse :
5) f(x) = x² - 2 x - 3 ⇒ f(x) = 0
Δ = 4 + 12 = 16 ⇒√16 = 4
x1 = 2 + 4)/2 = 3
x2 = 2-4)/2 = - 1
x - ∞ - 1 3 + ∞
f(x) + 0 - 0 +
6) f(x) = - x² - 5 x - 4
Δ = 25 - 16 = 9 ⇒ √9 = 3
x1 = 5 + 3)/-2 = - 4
x2 = 5-3)/-2 = - 1
x - ∞ - 4 - 1 + ∞
f(x) - 0 + 0 -
7) f(x) = 2 x² + x - 15
Δ = 1 + 120 = 121 ⇒ √121 = 11
x1 = - 1+11)/4 = 10/4 = 5/2
x2 = - 1-11)/4 = - 3
x - ∞ - 3 5/2 + ∞
f(x) + 0 - 0 +
8) f(x) = - 5 x² + 37 x + 54
Δ = 1369 + 1080 = 2449 ⇒ √2449 ≈ 49.5
x1 = - 37 + 49.5)/- 10 = - 1.25
x2 = - 37 - 49.5)/- 10 = 8.65
x - ∞ - 1.25 8.65 + ∞
f(x) - 0 + 0 -
Explications étape par étape
