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Beliebt Algebra >

6z^4-25z^3+32z^2+3z-10=0

Lösung

6 z^{4} - 25 z^{3} + 32 z^{2} + 3 z - 10 = 0

Lösung

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

Schritte zur Lösung

6 z^{4} - 25 z^{3} + 32 z^{2} + 3 z - 10 = 0

Faktorisiere

6 z^{4} - 25 z^{3} + 32 z^{2} + 3 z - 10 : (2 z + 1) (3 z - 2) (z^{2} - 4 z + 5)

(2 z + 1) (3 z - 2) (z^{2} - 4 z + 5) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

2 z + 1 = 0 or 3 z - 2 = 0 or z^{2} - 4 z + 5 = 0

Löse

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

Löse

3 z - 2 = 0 : z = \frac{2}{3}

Löse

z^{2} - 4 z + 5 = 0 : z = 2 + i, z = 2 - i

Die Lösungen sind

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

Graph

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8 x^{3} - 52 x^{2} + 78 x - 27 = 0

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