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Beliebt Algebra >

9x^4-3x^3+34x^2-12x-8=0

Lösung

9 x^{4} - 3 x^{3} + 34 x^{2} - 12 x - 8 = 0

Lösung

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

Schritte zur Lösung

9 x^{4} - 3 x^{3} + 34 x^{2} - 12 x - 8 = 0

Faktorisiere

9 x^{4} - 3 x^{3} + 34 x^{2} - 12 x - 8 : (3 x + 1) (3 x - 2) (x^{2} + 4)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

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

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

a^{3} - 44 a + 48 = 0

x^{3} + x = 0

x + x^{3} = 0

(x + 1)^{3} = 64

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