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Beliebt Algebra >

45z^3+18z^2-5z-2=0

Lösung

45 z^{3} + 18 z^{2} - 5 z - 2 = 0

Lösung

z = - \frac{2}{5}, z = - \frac{1}{3}, z = \frac{1}{3}

+1

Dezimale

z = - 0.4, z = - 0.33333 \dots, z = 0.33333 \dots

Schritte zur Lösung

45 z^{3} + 18 z^{2} - 5 z - 2 = 0

Faktorisiere

45 z^{3} + 18 z^{2} - 5 z - 2 : (5 z + 2) (3 z + 1) (3 z - 1)

(5 z + 2) (3 z + 1) (3 z - 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

5 z + 2 = 0 or 3 z + 1 = 0 or 3 z - 1 = 0

Löse

5 z + 2 = 0 : z = - \frac{2}{5}

Löse

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

Löse

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

Die Lösungen sind

z = - \frac{2}{5}, z = - \frac{1}{3}, z = \frac{1}{3}

Graph

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