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Beliebt Algebra >

3x^3+4x^2+4x+1=0

Lösung

3 x^{3} + 4 x^{2} + 4 x + 1 = 0

Lösung

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

Schritte zur Lösung

3 x^{3} + 4 x^{2} + 4 x + 1 = 0

Faktorisiere

3 x^{3} + 4 x^{2} + 4 x + 1 : (3 x + 1) (x^{2} + x + 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

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

Graph

Beliebte Beispiele

x^{4} = 27 x

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

x^{4} + 3 x^{2} - 28 = 0

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

512 x^{3} = 8