persamaan kuadrat

koreksi soal

persamaan kudarat baru yang akar akarnya (a + 1) dan (b + 1)

▪︎cara pertama

2x² - 5x - 7 = 0

a = 2, b = -5, c = -7

x¹ + x² = -b/a = 5/2

x¹.x² = c/a = -7/2

α + β = (a + 1) + (b + 1)

α + β = (a + b) + 2

α + β = (5/2) + 2

α + β = 9/2

α.β = (a + 1)(b + 1)

α.β = a.b + a + b + 1

α.β = (a.b) + (a + b) + 1

α.β = (-7/2) + (5/2) + 1

α.β = -2/2 + 1

α.β = 0

persamaan kuadrat baru :

x² - 9/2x + 0 = 0

2x² - 9x = 0 → persamaan kuadrat baru

• cara kedua

invers dari a + 1 → a - 1

subsitusi a - 1 ke persamaan lama :

2x² - 5x - 7 = 0

2(a - 1)² - 5(a - 1) - 7 = 0

2. a² - 2a + 1 - 5a + 5 - 7 = 0

2a² - 4a + 2 - 5a - 2 = 0

2a² - 9a = 0

2x² - 9x = 0 → persamaan kuadrat baru