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Beliebt Algebra >

x^4+2x^3+2x^2+2x+1=0

Lösung

x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1 = 0

Lösung

x = - 1, x = i, x = - i

Schritte zur Lösung

x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 1 = 0

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 1 = 0 : x = - 1

Löse

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

Die Lösungen sind

x = - 1, x = i, x = - i

Graph

Beliebte Beispiele

3 x^{3} - 4 = 0

b^{4} + 7 b^{2} - 18 = 0

(m^2+7m)^2+5(m^2+7m)-6=0

(m^{2} + 7 m)^{2} + 5 (m^{2} + 7 m) - 6 = 0

3x^3+9x^2-120x=0

3 x^{3} + 9 x^{2} - 120 x = 0

9 x^{2} - 14 x - x^{3} = 0