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Beliebt Algebra >

3z^3-2z^2+2z+1=0

Lösung

3 z^{3} - 2 z^{2} + 2 z + 1 = 0

Lösung

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

Schritte zur Lösung

3 z^{3} - 2 z^{2} + 2 z + 1 = 0

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

3 z + 1 = 0 : z = - \frac{1}{3}

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

Graph

Beliebte Beispiele

u^{4} - 5 u^{2} + 6 = 0

8x^3-12x^2-24x=0

8 x^{3} - 12 x^{2} - 24 x = 0

x^{3} + 9 x - 8 = 0

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

x^4+x^3+2x^2-x=4.1151

x^{4} + x^{3} + 2 x^{2} - x = 4.1151