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Beliebt Algebra >

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

Lösung

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

Lösung

x = - 1, x = 1, x = 1 + i, x = 1 - i

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 1 = 0 : x = - 1

Löse

x - 1 = 0 : x = 1

Löse

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

Die Lösungen sind

x = - 1, x = 1, x = 1 + i, x = 1 - i

Graph

Beliebte Beispiele

solvefor z,(a)z^4=24i-7

so l v e f or z, (a) z^{4} = 24 i - 7

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

- 1 + v^{3} = - 3

x (x + 3) (x - 2) = 0

x^3+6x^2-36x+2=0

x^{3} + 6 x^{2} - 36 x + 2 = 0