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Beliebt Algebra >

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

Lösung

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

Lösung

x = 0, x = 3, x = - 2, x = 2

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x - 3 = 0 or x + 2 = 0 or x - 2 = 0

Löse

x - 3 = 0 : x = 3

Löse

x + 2 = 0 : x = - 2

Löse

x - 2 = 0 : x = 2

Die Lösungen sind

x = 0, x = 3, x = - 2, x = 2

Graph

Beliebte Beispiele

3 x^{4} - 3 = 0

- 9 = - 1 + 8 x^{3}

r^4+4r^3+6r^2+4r+1=0

r^{4} + 4 r^{3} + 6 r^{2} + 4 r + 1 = 0

x^4-5x^3+6x^2=0

x^{4} - 5 x^{3} + 6 x^{2} = 0

y^{3} + y^{2} = 9 y + 9