Réponse :
Explications étape par étape
Bonjour,
résoudre les équations proposées en utilisant la formule du discriminant :
x² - 7x + 10 = 0
Δ = (-7)² - 4 * 1 * 10 = 49 - 40 = 9 = 3²
√Δ = 3
x₁ = (7 - 3)/(2 * 1) = 4/2 = 2
x₂ = (7 + 3)/(2 * 1) = 10/2 = 5
S = {2 ; 5}
x² + 8x + 16 = 0
Δ = (8)² - 4 * 1 * 16 = 64 - 64 = 0
√Δ = 0
x₁ = x₂ = 8/(2 * 1) = 8/2 = 4
S = {4}
x² - 10x + 16 = 0
Δ = (-10)² - 4 * 1 * 16 = 100 - 64 = 36 = 6²
√Δ = 6
x₁ = (10 - 6)/(2 * 1) = 4/2 = 2
x₂ = (10 + 6)/(2 * 1) = 16/2 = 8
S = {2 ; 8}
9x² - 12x + 4 = 0
Δ = (-12)² - 4 * 9 * 4 = 144 - 144 = 0
√Δ = 0
x₁ = x₂ = 12/(2 * 9) = 12/18 = 2/3
S = {2/3}
-x² + 4x - 3 = 0
Δ = (4)² - 4 * (-1) * (-3) = 16 - 12 = 4 = 2²
√Δ = 2
x₁ = (-4 - 2)/(2 * -1) = -6/-2 = 3
x₂ = (-4 + 2)/(2 * -1) = -2/-2 = 1
S = {1 ; 3}
-x² + 5x - 6 = 0
Δ = (5)² - 4 * (-1) * (-6) = 25 - 24 = 1 = 1²
√Δ = 1
x₁ = (-5 - 1)/(2 * -1) = -6/-2 = 3
x₂ = (-5 + 1)/(2 * -1) = -4/-2 = 2
S = {2 ; 3}
