Odpowiedzi

2009-10-03T15:57:54+02:00
Założenia
W(x) = x³ - x² - 4x + 4

teza:
x_1 + x_2 + x_3 = 1

dowód:
W(x) = x³ - x² - 4x + 4 = (x³ - 4x) - (x² - 4) = x(x² - 4) - (x² - 4) = (x² - 4)(x - 1) = (x - 2)(x + 2)*(x - 1)

pieswiastki:
x_1 = -2
x_2 = 1
x_3 = 2

suma:
x_1 + x_2 + x_3 = -2 + 1 + 2 = 1
2009-10-03T16:22:19+02:00
(x³-x²-4x+4) : (x-1) = x²-4

(x-2)(x+2)(x-1)
x1= 2 ; x2 = -2 x3 = 1