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Beliebt Algebra >

3x^4+8x^3+6x^2+3x-2=0

Lösung

3 x^{4} + 8 x^{3} + 6 x^{2} + 3 x - 2 = 0

Lösung

x = - 2, 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^{4} + 8 x^{3} + 6 x^{2} + 3 x - 2 = 0

Faktorisiere

3 x^{4} + 8 x^{3} + 6 x^{2} + 3 x - 2 : (x + 2) (3 x - 1) (x^{2} + x + 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 2 = 0 : x = - 2

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

Graph

Beliebte Beispiele

2 x^{4} - 200 x^{2} = 0

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x^{3} + x^{2} - 9 x + 9 = 0