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Beliebt Algebra >

3x^3+x^2+x-2=0

Lösung

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

Lösung

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

Schritte zur Lösung

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

Faktorisiere

3 x^{3} + x^{2} + x - 2 : (3 x - 2) (x^{2} + x + 1)

(3 x - 2) (x^{2} + x + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

3 x - 2 = 0 or x^{2} + x + 1 = 0

Löse

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

Löse

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

Die Lösungen sind

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

Graph

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