Oi, boa noite!
Resposta:
A) S = {– 4, 5}.
B) S = {(– 1)/4}.
C) S = ∅.
D) S = {0, 10}.
E) S = ∅.
F) S = {– 2, 2}.
Explicação passo-a-passo:
A) x² – x – 20 = 0.
a = 1, b = – 1 e c = – 20.
Δ = b² – 4 · a · c
Δ = (– 1)² – 4 · 1 · (– 20)
Δ = 1 + 80
Δ = 81.
x = (– b ± √Δ)/(2 · a)
x = [–(– 1) ± √81]/(2 · 1)
x = [1 ± 9]/2
x = (1 ± 9)/2.
x₁ = (1 + 9)/2
x₁ = 10/2
x₁ = 5.
x₂ = (1 – 9)/2
x₂ = (– 8)/2
x₂ = – 4.
S = {– 4, 5}.
B) 16x² + 8x + 1 = 0.
a = 16, b = 8 e c = 1.
Δ = b² – 4 · a · c
Δ = 8² – 4 · 16 · 1
Δ = 64 + 64
Δ = 0.
x = (– b)/(2 · a)
x = (– 8)/(2 · 16)
x = (– 8)/32 ---> Simplificando "(– 8)/32" por 8:
x = (– 1)/4.
S = {(– 1)/4}.
C) 2x² – 4x + 12 = 0.
a = 2, b = – 4 e c = 12.
Δ = b² – 4 · a · c
Δ = (– 4)² – 4 · 2 · 12
Δ = 16 – 96
Δ = – 80.
S = ∅.
D) x² – 10x = 0
x · (x – 10) = 0.
x = 0.
x – 10 = 0
x = 0 + 10
x = 10.
x₁ = 0 e x₂ = 10.
S = {0, 10}.
E) 3x² – 3x + 3 = 0.
a = 3, b = – 3 e c = 3.
Δ = b² – 4 · a · c
Δ = (– 3)² – 4 · 3 · 3
Δ = 9 – 36
Δ = – 25.
S = ∅.
F) x² – 4 = 0
x² = 0 + 4
x² = 4
x = ± √4
x = ± 2. ---> x₁ = – 2 e x₂ = 2.
S = {– 2, 2}.
Espero ter te ajudado e bons estudos para você! ;)
