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Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 2 = 0 : x = - 2

Löse

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

Graph

Beliebte Beispiele

18 x^{2} - 9 x^{4} = 0

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

y (2 - y) (4 - y) = 0

x^{3} - 10 = 7

y^{4} + 5 y^{2} - 36 = 0