Oi, boa noite!
Resposta:
1) A) S = {5, 3}.
B) S = {– 5}.
C) S = ∅.
D) S = {4, 3}.
E) S = ∅.
Explicação passo-a-passo:
1) A) x² – 8x + 15 = 0.
a = 1, b = – 8 e c = 15.
Δ = b² – 4 · a · c
Δ = (– 8)² – 4 · 1 · 15
Δ = 64 – 60
Δ = 4.
x = (– b ± √Δ)/(2 · a)
x = [–(– 8) ± √4]/(2 · 1)
x = (8 ± 2)/2.
x₁ = (8 + 2)/2
x₁ = 10/2
x₁ = 5.
x₂ = (8 – 2)/2
x₂ = 6/2
x₂ = 3.
S = {5, 3}.
B) x² + 10x + 25 = 0.
a = 1, b = 10 e c = 25.
Δ = b² – 4 · a · c
Δ = 10² – 4 · 1 · 25
Δ = 100 – 100
Δ = 0.
x = (– b)/(2 · a)
x = (– 10)/(2 · 1)
x = (– 10)/2
x = – 5.
S = {– 5}.
C) 3x² + 4x + 1 = 0.
a = 3, b = 4 e c = 1.
Δ = b² – 4 · a · c
Δ = 4² – 4 · 1 · 15
Δ = 16 – 60
Δ = – 44.
S = ∅.
D) x² – 7x + 12 = 0.
a = 1, b = – 7 e c = 12.
Δ = b² – 4 · a · c
Δ = (– 7)² – 4 · 1 · 12
Δ = 49 – 48
Δ = 1.
x = (– b ± √Δ)/(2 · a)
x = [–(– 7) ± √1]/(2 · 1)
x = (7 ± 1)/2.
x₁ = (7 + 1)/2
x₁ = 8/2
x₁ = 4.
x₂ = (7 – 1)/2
x₂ = 6/2
x₂ = 3.
S = {4, 3}.
E) x² – 4x + 5 = 0.
a = 1, b = – 4 e c = 5.
Δ = b² – 4 · a · c
Δ = (– 4)² – 4 · 1 · 5
Δ = 16 – 20
Δ = – 4.
S = ∅.
Espero ter te ajudado e bons estudos para você! ;)
