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Beliebt Algebra >

z^7-9z^4+8z=0

Lösung

z^{7} - 9 z^{4} + 8 z = 0

Lösung

z = 0, z = 1, z = 2, z = - \frac{1}{2} + i \frac{3}{2}, z = - \frac{1}{2} - i \frac{3}{2}, z = - 1 + 3 i, z = - 1 - 3 i

Schritte zur Lösung

z^{7} - 9 z^{4} + 8 z = 0

Faktorisiere

z^{7} - 9 z^{4} + 8 z : z (z - 1) (z - 2) (z^{2} + z + 1) (z^{2} + 2 z + 4)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

z = 0 or z - 1 = 0 or z - 2 = 0 or z^{2} + z + 1 = 0 or z^{2} + 2 z + 4 = 0

Löse

z - 1 = 0 : z = 1

Löse

z - 2 = 0 : z = 2

Löse

z^{2} + z + 1 = 0 : z = - \frac{1}{2} + i \frac{3}{2}, z = - \frac{1}{2} - i \frac{3}{2}

Löse

z^{2} + 2 z + 4 = 0 : z = - 1 + 3 i, z = - 1 - 3 i

Die Lösungen sind

z = 0, z = 1, z = 2, z = - \frac{1}{2} + i \frac{3}{2}, z = - \frac{1}{2} - i \frac{3}{2}, z = - 1 + 3 i, z = - 1 - 3 i

Graph

Beliebte Beispiele

x^{3} = \frac{27}{64}

2x^3-9x^2-24x+20=0

2 x^{3} - 9 x^{2} - 24 x + 20 = 0

x^{4} + 10 x^{2} + 25 = 0

2x^3-3x^2-9x+10=0

2 x^{3} - 3 x^{2} - 9 x + 10 = 0

solvefor x,y=27x^3

so l v e f or x, y = 27 x^{3}