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Beliebt Algebra >

15z^5-35z^2=0

Lösung

15 z^{5} - 35 z^{2} = 0

Lösung

z = 0, z = 3 \frac{7}{3}, z = - 3 \frac{7}{3} \frac{1}{2} + 3 \frac{7}{3} \frac{3}{2} i, z = - 3 \frac{7}{3} \frac{1}{2} - 3 \frac{7}{3} \frac{3}{2} i

Schritte zur Lösung

15 z^{5} - 35 z^{2} = 0

Faktorisiere

15 z^{5} - 35 z^{2} : 5 z^{2} (3 z^{3} - 7)

5 z^{2} (3 z^{3} - 7) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

z = 0 or 3 z^{3} - 7 = 0

Löse

3 z^{3} - 7 = 0 : z = 3 \frac{7}{3}, z = - 3 \frac{7}{3} \frac{1}{2} + 3 \frac{7}{3} \frac{3}{2} i, z = - 3 \frac{7}{3} \frac{1}{2} - 3 \frac{7}{3} \frac{3}{2} i

Die Lösungen sind

z = 0, z = 3 \frac{7}{3}, z = - 3 \frac{7}{3} \frac{1}{2} + 3 \frac{7}{3} \frac{3}{2} i, z = - 3 \frac{7}{3} \frac{1}{2} - 3 \frac{7}{3} \frac{3}{2} i

Graph

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