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Beliebt Algebra >

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

Lösung

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

Lösung

x = 2, x = - \frac{1}{2} + i \frac{11}{2}, x = - \frac{1}{2} - i \frac{11}{2}

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 2 = 0 : x = 2

Löse

x^{2} + x + 3 = 0 : x = - \frac{1}{2} + i \frac{11}{2}, x = - \frac{1}{2} - i \frac{11}{2}

Die Lösungen sind

x = 2, x = - \frac{1}{2} + i \frac{11}{2}, x = - \frac{1}{2} - i \frac{11}{2}

Graph

Beliebte Beispiele

(6 x + 9)^{3} + 3 = 0

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

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

2x^3-3x^2-3x-2=0

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

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

5^2x-3-2(x^5)^2=5^2x^3

5^{2} x - 3 - 2 (x^{5})^{2} = 5^{2} x^{3}