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Beliebt Algebra >

x^4+x^3-x^2+x-2=0

Lösung

x^{4} + x^{3} - x^{2} + x - 2 = 0

Lösung

x = 1, x = - 2, x = i, x = - i

Schritte zur Lösung

x^{4} + x^{3} - x^{2} + x - 2 = 0

Faktorisiere

x^{4} + x^{3} - x^{2} + x - 2 : (x - 1) (x + 2) (x^{2} + 1)

(x - 1) (x + 2) (x^{2} + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 1 = 0 or x + 2 = 0 or x^{2} + 1 = 0

Löse

x - 1 = 0 : x = 1

Löse

x + 2 = 0 : x = - 2

Löse

x^{2} + 1 = 0 : x = i, x = - i

Die Lösungen sind

x = 1, x = - 2, x = i, x = - i

Graph

Beliebte Beispiele

x^{10} = 20

2a^2-a-2=0.8a^6-13a^3-3

2 a^{2} - a - 2 = 0.8 a^{6} - 13 a^{3} - 3

x^{3} + 2 x^{2} - x + 2 = 0

x^{10} = - x

-x^3+9x^2-24x+20=0

- x^{3} + 9 x^{2} - 24 x + 20 = 0