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2009-10-24T21:45:21+02:00
X₁=-3
x₂=1
W(x) = x³ + ax² = bx - 9
W(x) = x³ + ax² - bx + 9
0 = (-3)³ + a(-3)² -b(-3) +9 ∧ 0 = 1³ +a*1² - b*1 +9
0 = -27 + 9a + 3b +9 ∧ 0 = 1 + a - b + 9
0 = -18 + 9a + 3b ∧ 0 = 10 + a - b
b = 10 + a ∧ 0 = -18 + 9a + 3(10 + a)
0 = -18 + 9a + 30 + 3a
-12 = 12a
a = -1 ∧ b = 9

W(x) = x³ - x² - 9x + 9
x³ - x² - 9x + 9 = 0
x²(x-1) - 9(x-1) = 0
(x²-9)(x-1) = 0 {(x²-9) = (x-3)(x+3) ze wzoru (a²-b²)=(a-b)(a+b)}
(x-3)(x+3)(x-1) = 0

x₃=3