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Beliebt Algebra >

6x^4-x^3+5x^2-x-1=0

Lösung

6 x^{4} - x^{3} + 5 x^{2} - x - 1 = 0

Lösung

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

Schritte zur Lösung

6 x^{4} - x^{3} + 5 x^{2} - x - 1 = 0

Faktorisiere

6 x^{4} - x^{3} + 5 x^{2} - x - 1 : (2 x - 1) (3 x + 1) (x^{2} + 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

2 x - 1 = 0 : x = \frac{1}{2}

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

solvefor y,x=y^3+1

so l v e f or y, x = y^{3} + 1

2 x^{4} - 3 x^{2} - 20 = 0

x^{8} - 8 = 0

x^{4} - 3 x^{2} = - 2

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