Question

Rozwiąż równania :
a) x^3 + x^2 - 6x = 0
b) x^3 + 5x^2 -x - 5 = 0

Answer 1

A)
x³ + x² - 6x = 0
x(x² + x - 6) = 0
x = 0 lib x² + x - 6 = 0
x² + x - 6 = 0
Δ = 1 - 4 * 1 * (- 6) = 1 + 24 = 25
√Δ = √25 = 5
x₁ = (- 1 - 5)/2 = - 6/2 = - 3
x₂ = (- 1 + 5)/2 = 4/2 = 2
odp
x = 0 lub x = - 3 lub x = 2
b)
x³ + 5x² - x - 5 = 0
x²(x + 5) - (x + 5) = 0
(x + 5)(x² - 1) = 0
(x + 5)(x - 1)(x + 1) = 0
odp
x = - 5 lub x = 1 lub x = - 1