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Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 1 = 0 : x = 1

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

Graph

Beliebte Beispiele

3x^3+2x-1=8x^2-4

3 x^{3} + 2 x - 1 = 8 x^{2} - 4

18 x^{3} + 90 x + 55 = 0

x^{4} + x - 4 = 0

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

x^3-2x^2-6x+12=0

x^{3} - 2 x^{2} - 6 x + 12 = 0