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Beliebt Algebra >

6x^4-7x^3-x^2+67x-105=0

Lösung

6 x^{4} - 7 x^{3} - x^{2} + 67 x - 105 = 0

Lösung

x = \frac{3}{2}, x = - \frac{7}{3}, x = 1 + 2 i, x = 1 - 2 i

Schritte zur Lösung

6 x^{4} - 7 x^{3} - x^{2} + 67 x - 105 = 0

Faktorisiere

6 x^{4} - 7 x^{3} - x^{2} + 67 x - 105 : (2 x - 3) (3 x + 7) (x^{2} - 2 x + 5)

(2 x - 3) (3 x + 7) (x^{2} - 2 x + 5) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

2 x - 3 = 0 or 3 x + 7 = 0 or x^{2} - 2 x + 5 = 0

Löse

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

Löse

3 x + 7 = 0 : x = - \frac{7}{3}

Löse

x^{2} - 2 x + 5 = 0 : x = 1 + 2 i, x = 1 - 2 i

Die Lösungen sind

x = \frac{3}{2}, x = - \frac{7}{3}, x = 1 + 2 i, x = 1 - 2 i

Graph

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