kal to rozwiązać
x^3 - x^2 + 2 = 0
x^3 + x^2 - 2x^2 + 2 = 0
x^2(x + 1) - 2(x^2 - 1) = 0
x^2(x + 1) - 2(x - 1)(x + 1) = 0
(x + 1) [ x^2 - 2(x - 1) ] = 0
(x +1) (x^2 - 2x + 2) = 0
Δ = 2 - 8 = - 6 < 0
x + 1 = 0
x = -1
x³-x²+2 = 0
x³+x²-2x²+2 = 0
x²(x+1) - 2(x²-1) = 0
x²(x+1) - 2(x+1)(x-1) = 0
(x+1)[x²-2(x-1)] = 0
x=1 = 0
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v
x²-2x+2 = 0
Δ = b²-4ac = 4-8 = -4
Δ < 0, zatem brak pierwiastków równania.
Odp. x = -1
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x^3 - x^2 + 2 = 0
x^3 + x^2 - 2x^2 + 2 = 0
x^2(x + 1) - 2(x^2 - 1) = 0
x^2(x + 1) - 2(x - 1)(x + 1) = 0
(x + 1) [ x^2 - 2(x - 1) ] = 0
(x +1) (x^2 - 2x + 2) = 0
Δ = 2 - 8 = - 6 < 0
x + 1 = 0
x = -1
x³-x²+2 = 0
x³+x²-2x²+2 = 0
x²(x+1) - 2(x²-1) = 0
x²(x+1) - 2(x+1)(x-1) = 0
(x+1)[x²-2(x-1)] = 0
x=1 = 0
x = -1
=====
v
x²-2x+2 = 0
Δ = b²-4ac = 4-8 = -4
Δ < 0, zatem brak pierwiastków równania.
Odp. x = -1