Odpowiedź:
a)
x³ - 6x² + 8x = 0
x(x² - 6x + 8) = 0
x = 0 ∨ x² - 6x + 8 = 0
x² - 6x + 8 = 0
Δ = (- 6)² - 4 * 1 * 8 = 36 - 32 = 4
√Δ = √4 = 2
x₁ = (6 - 2)/2 = 4/2 = 2
x₂ = (6 + 2)/2 = 8/2 = 4
x = 0 ∨ x = 2 ∨ x = 4
b)
x³ - 4x² - 12x = 0
x(x² - 4x - 12) = 0
x = 0 ∨ x² - 4x - 12 = 0
x² - 4x - 12 = 0
Δ = (- 4)²- 4 * 1 * (- 12)= 16 + 48 = 64
√Δ = √64 = 8
x₁ = (4 - 8)/2 = (- 4)/2 = - 2
x₂ = (4 + 8)/2 = 12/2 = 6
x =0 ∨ x = - 2 ∨ x = 6
c)
4x³ - 7x² - 2x = 0
x(4x² - 7x - 2) = 0
x = 0 ∨ 4x² - 7x - 2 = 0
4x² - 7x - 2 = 0
Δ = (- 7)² - 4 * 4 * (- 2) = 49 + 32 = 81
√Δ = √81 = 9
x₁ = (7 - 9)/8 = (- 2)/8 = - 1/4
x₂ = (7 + 9)/8 = 16/8 = 2
x = 0 ∨ x = - 1/4 ∨ x = 2
d)
2x³ + 4x² + x = 0
x(2x² + 4x + 1) = 0
x =0 ∨ 2x² + 4x + 1 =0
2x² + 4x +1 =0
Δ = 4² - 4 * 2 * 1 = 16 - 8 = 8
√Δ = √8 = 2√2
x₁ =(- 4 - 2√2)/4 = - 2(2 + √2)/4 = - (2 + √2)/2
x₂ = (- 4 + 2√2)/4 = 2(√2 - 2)/4 = (√2 - 2)/2
x = 0 ∨ x = - (2 + √2)/2 ∨ x = (√2 - 2)/2
Szczegółowe wyjaśnienie:
