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Beliebt Algebra >

x^4-x^3+3x^2-9x-54=0

Lösung

x^{4} - x^{3} + 3 x^{2} - 9 x - 54 = 0

Lösung

x = - 2, x = 3, x = 3 i, x = - 3 i

Schritte zur Lösung

x^{4} - x^{3} + 3 x^{2} - 9 x - 54 = 0

Faktorisiere

x^{4} - x^{3} + 3 x^{2} - 9 x - 54 : (x + 2) (x - 3) (x^{2} + 9)

(x + 2) (x - 3) (x^{2} + 9) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 2 = 0 or x - 3 = 0 or x^{2} + 9 = 0

Löse

x + 2 = 0 : x = - 2

Löse

x - 3 = 0 : x = 3

Löse

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

Die Lösungen sind

x = - 2, x = 3, x = 3 i, x = - 3 i

Graph

Beliebte Beispiele

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

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

2x^3+5x^2+32x+80=0

2 x^{3} + 5 x^{2} + 32 x + 80 = 0

0 = x^{4}

t^{4} - 81 = 0

y^{4} = y^{2}