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Beliebt Algebra >

4z^5-14z^2=0

Lösung

4 z^{5} - 14 z^{2} = 0

Lösung

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

Schritte zur Lösung

4 z^{5} - 14 z^{2} = 0

Faktorisiere

4 z^{5} - 14 z^{2} : 2 z^{2} (2 z^{3} - 7)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

z = 0 or 2 z^{3} - 7 = 0

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

x^{3} + 5 x + 2 = 0

81 = r^{4}

solvefor x,3x^3+y^4=cy

so l v e f or x, 3 x^{3} + y^{4} = cy

x^{5} - x^{3} - 3 x - 2 = 0

x^{3} - 15 = - 7