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Beliebt Algebra >

80z^4-4z^3-6z^2-4z-1=0

Lösung

80 z^{4} - 4 z^{3} - 6 z^{2} - 4 z - 1 = 0

Lösung

z = \frac{1}{2}, z = - \frac{1}{4}, z = - \frac{1}{10} + i \frac{3}{10}, z = - \frac{1}{10} - i \frac{3}{10}

Schritte zur Lösung

80 z^{4} - 4 z^{3} - 6 z^{2} - 4 z - 1 = 0

Faktorisiere

80 z^{4} - 4 z^{3} - 6 z^{2} - 4 z - 1 : (2 z - 1) (4 z + 1) (10 z^{2} + 2 z + 1)

(2 z - 1) (4 z + 1) (10 z^{2} + 2 z + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

2 z - 1 = 0 or 4 z + 1 = 0 or 10 z^{2} + 2 z + 1 = 0

Löse

2 z - 1 = 0 : z = \frac{1}{2}

Löse

4 z + 1 = 0 : z = - \frac{1}{4}

Löse

10 z^{2} + 2 z + 1 = 0 : z = - \frac{1}{10} + i \frac{3}{10}, z = - \frac{1}{10} - i \frac{3}{10}

Die Lösungen sind

z = \frac{1}{2}, z = - \frac{1}{4}, z = - \frac{1}{10} + i \frac{3}{10}, z = - \frac{1}{10} - i \frac{3}{10}

Graph

Beliebte Beispiele

665 = 5 x^{3}

p^{3} - 16 p = 0

x^{4} - 5 x^{2} = 0

0 = (x + 2)^{3}

s^3+5s^2+3s+1=0

s^{3} + 5 s^{2} + 3 s + 1 = 0