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}