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Beliebt Algebra >

x^4-3x^3-2x^2+10x-12=0

Lösung

x^{4} - 3 x^{3} - 2 x^{2} + 10 x - 12 = 0

Lösung

x = - 2, x = 3, x = 1 + i, x = 1 - i

Schritte zur Lösung

x^{4} - 3 x^{3} - 2 x^{2} + 10 x - 12 = 0

Faktorisiere

x^{4} - 3 x^{3} - 2 x^{2} + 10 x - 12 : (x + 2) (x - 3) (x^{2} - 2 x + 2)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 2 = 0 : x = - 2

Löse

x - 3 = 0 : x = 3

Löse

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

Die Lösungen sind

x = - 2, x = 3, x = 1 + i, x = 1 - i

Graph

Beliebte Beispiele

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

x^{4} - 256 = 0

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

x^{5} + x^{3} + x = 3

16m^4+24m^2+9=0

16 m^{4} + 24 m^{2} + 9 = 0