Mathématiques

Question

bonjour svp 4 equation du second degré a resoudre j'y comprend rien

" = au carré

a) x" + 4x - 12 = 0

b) x" + 8x + 16 = 0

c) x" + 4x + 5 = 0

d) x" - 4x - 2 = 0

1 Réponse

  • x² + 4x - 12 = 0

    Δ = b²-4ac
    Δ = 4²-4*1*(-12)
    Δ = 16+48
    Δ = 64

    √Δ = √64 = 8

    x₁ = (-b-√Δ)/2a = (-4-8)/2*1 = -12/2 = -6
    x₂ = (-b+√Δ)/2a = (-4+8)/2*1 = 4/2 = 2

    x² + 8x + 16 = 0

    Δ = 8²-4*1*16
    Δ = 64 - 64
    Δ = 0

    x₀ = -b/2a = -8/2*1 = -8/2 = -4

    x² + 4x + 5 = 0 

    Δ = 4²-4*1*5
    Δ = 16 - 20
    Δ = -4
    Δ < 0

    Pas de solution réelle 

    x² - 4x - 2 = 0

    Δ = (-4)²-4*1*(-2)
    Δ = 16+8
    Δ = 24

    x₁ = (-b-√Δ)/2a = (4-√24)/2
    x₂ = (-b+√Δ)/2a = (4+√24)/2 

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