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Beliebt Algebra >

x^4-4x^3+7x^2-6x-18=0

Lösung

x^{4} - 4 x^{3} + 7 x^{2} - 6 x - 18 = 0

Lösung

x = - 1, x = 3, x = 1 + 5 i, x = 1 - 5 i

Schritte zur Lösung

x^{4} - 4 x^{3} + 7 x^{2} - 6 x - 18 = 0

Faktorisiere

x^{4} - 4 x^{3} + 7 x^{2} - 6 x - 18 : (x + 1) (x - 3) (x^{2} - 2 x + 6)

(x + 1) (x - 3) (x^{2} - 2 x + 6) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or x - 3 = 0 or x^{2} - 2 x + 6 = 0

Löse

x + 1 = 0 : x = - 1

Löse

x - 3 = 0 : x = 3

Löse

x^{2} - 2 x + 6 = 0 : x = 1 + 5 i, x = 1 - 5 i

Die Lösungen sind

x = - 1, x = 3, x = 1 + 5 i, x = 1 - 5 i

Graph

Beliebte Beispiele

x^{3} - 5 x^{2} = - 4 x

3 x^{6} - 14 x^{3} = 80

6 x^{2} x = 2

x^{8} = xx + 5

270x-3x^2-3x^3=0

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