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Beliebt Algebra >

z^3+z^2+z=0

Lösung

z^{3} + z^{2} + z = 0

Lösung

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

Schritte zur Lösung

z^{3} + z^{2} + z = 0

Faktorisiere

z^{3} + z^{2} + z : z (z^{2} + z + 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

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

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

7x^3-47x^2+121x-65=0

7 x^{3} - 47 x^{2} + 121 x - 65 = 0

x^{2} - 4 = x^{3} - 2 x^{2}

(x^2-2)^2-4(x^2-2)+4=0

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

x^{4} + x^{2} = \frac{4}{5}