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Beliebt Algebra >

x^4-8x^3+24x^2-32x=0

Lösung

x^{4} - 8 x^{3} + 24 x^{2} - 32 x = 0

Lösung

x = 0, x = 4, x = 2 + 2 i, x = 2 - 2 i

Schritte zur Lösung

x^{4} - 8 x^{3} + 24 x^{2} - 32 x = 0

Faktorisiere

x^{4} - 8 x^{3} + 24 x^{2} - 32 x : x (x - 4) (x^{2} - 4 x + 8)

x (x - 4) (x^{2} - 4 x + 8) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x - 4 = 0 or x^{2} - 4 x + 8 = 0

Löse

x - 4 = 0 : x = 4

Löse

x^{2} - 4 x + 8 = 0 : x = 2 + 2 i, x = 2 - 2 i

Die Lösungen sind

x = 0, x = 4, x = 2 + 2 i, x = 2 - 2 i

Graph

Beliebte Beispiele

x^{3} - 10 x + 21 = 0

x^{4} - 12 x^{2} + 16 = 0

2(x^2-2x)^2-5(x^2-2x)=6

2 (x^{2} - 2 x)^{2} - 5 (x^{2} - 2 x) = 6

729 = x^{3}

solvefor z,z^6+4z^3+16=0

so l v e f or z, z^{6} + 4 z^{3} + 16 = 0