Question

Tentukan persamaan kuadrat yang memiliki akar-akar =
A. -3 dan 5
B. 1 + √2 dan 1 - √2

Answer 1

Verified answer

Persamaan Kuadrat
Kelas X

a.
α = -3 , β = 5

α + β = -3 + 5 = 2
αβ = -3 × 5 = -15

Persamaannya
x² - (α + β)x + αβ = 0
x² - 2x - 15 = 0

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b.
α = 1 + √2 , β = 1 - √2

α + β = 1 + √2 + 1 - √2
= 2
αβ = (1 + √2)(1 - √2)
= 1² - (√2)²
= 1 - 2 = -1

Persamaannya
x² - (α + β)x + αβ = 0
x² - 2x - 1 = 0