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Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

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

Graph

Beliebte Beispiele

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

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

s^{3} = 729

x^3+5x^2-25x-125=0

x^{3} + 5 x^{2} - 25 x - 125 = 0

t^{3} - 9 t^{2} = 0