" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
Verified answer
Persamaan KuadratKelas X
2x² - 4x - 1 = 0 , akar²nya x₁ dan x₂
x₁ + x₂ = -b/a = -(-4) / 2 = 2
x₁x₂ = c/a = - ½
Persamaan baru yang akar²nya (x₁ - 2) dan (x₂ - 2)
(x₁ - 2) + (x₂ - 2) = (x₁ + x₂) - 4
= 2 - 4 = -2
(x₁ - 2)(x₂ - 2) = x₁x₂ - 2(x₁ + x₂) + 4
= - ½ - 2(2) + 4
= - ½
Persamaan yang baru :
x² - ((x₁ - 2) + (x₂ - 2))x + ((x₁ - 2)(x₂ - 2)) = 0
x² + 2x - ½ = 0 [× 2]
2x² + 4x - 1 = 0
Verified answer
Kelas : X SMAMapel : Matematika Wajib
Bab : Persamaan dan Fungsi Kuadrat
Indikator : Membuat Persamaan Kuadrat Baru
Langkah Penyelesaian dan Jawaban :
(x1 = α, x2 = β)
2x² - 4x - 1 = 0, memiliki akar α dan β, serta :
a = 2
b = - 4
c = - 1
α + β = - b/a
α + β = - (- 4) / 2
α + β = 2
αβ = c/a
αβ = - 1/2
- Membuat PK baru, jika (α - 2) dan (β - 2) :
α + β = (α - 2) + (β - 2)
α + β = α - 2 + β - 2
α + β = α + β - 4
α + β = 2 - 4
α + β = - 2
αβ = (α - 2) (β - 2)
αβ = αβ - 2a - 2β + 4
αβ = αβ - 2(α + β) + 4
αβ = - 1/2 - 2(2) + 4
αβ = - 1/2
x² - (α + β)x + αβ = 0
x² - (- 2)x - 1/2 = 0
x² + 2x - 1/2 = 0
2x² + 4x - 1 = 0