Persamaan kuadrat gres yg akar-
akarnya 3α – 1 & 3β – 1 yakni
2x² + 19x – 1 = 0
Pembahasan:
2x² + 5x – 2
mempunyai akar-akar α & β, maka
α + β = -5/2
α . β = -2/2 = -1
Persamaan kuadrat gres yg akar-akarnya 3α − 1 & 3β − 1 yaitu:
Misal:
3α − 1 = x₁
3β – 1 = x₂
x² – (x₁ + x₂)² + (x₁ . x₂) = 0
x² – [(3α − 1 ) + (3β − 1)]x + (3α − 1)(3β − 1) = 0
x² – (3α + 3β – 2)x + (9αβ – 3α – 3β + 1) = 0
x² – (3(α + β) – 2)x + (9αβ – 3(α + β) + 1) = 0
x² – (3(-5/2) – 2)x + (9(-1) – 3(-5/2) + 1 = 0
x² – (-19/2)x + (-½) = 0
2x² + 19 – 1 = 0