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Beliebt Algebra >

x^4-3x^3+5x^2-27x-36=0

Lösung

x^{4} - 3 x^{3} + 5 x^{2} - 27 x - 36 = 0

Lösung

x = - 1, x = 4, x = 3 i, x = - 3 i

Schritte zur Lösung

x^{4} - 3 x^{3} + 5 x^{2} - 27 x - 36 = 0

Faktorisiere

x^{4} - 3 x^{3} + 5 x^{2} - 27 x - 36 : (x + 1) (x - 4) (x^{2} + 9)

(x + 1) (x - 4) (x^{2} + 9) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or x - 4 = 0 or x^{2} + 9 = 0

Löse

x + 1 = 0 : x = - 1

Löse

x - 4 = 0 : x = 4

Löse

x^{2} + 9 = 0 : x = 3 i, x = - 3 i

Die Lösungen sind

x = - 1, x = 4, x = 3 i, x = - 3 i

Graph

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