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Beliebt Algebra >

x^5+x^3+8x^2+8=0

Lösung

x^{5} + x^{3} + 8 x^{2} + 8 = 0

Lösung

x = - 2, x = i, x = - i, x = 1 + 3 i, x = 1 - 3 i

Schritte zur Lösung

x^{5} + x^{3} + 8 x^{2} + 8 = 0

Faktorisiere

x^{5} + x^{3} + 8 x^{2} + 8 : (x + 2) (x^{2} + 1) (x^{2} - 2 x + 4)

(x + 2) (x^{2} + 1) (x^{2} - 2 x + 4) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 2 = 0 or x^{2} + 1 = 0 or x^{2} - 2 x + 4 = 0

Löse

x + 2 = 0 : x = - 2

Löse

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

Löse

x^{2} - 2 x + 4 = 0 : x = 1 + 3 i, x = 1 - 3 i

Die Lösungen sind

x = - 2, x = i, x = - i, x = 1 + 3 i, x = 1 - 3 i

Graph

Beliebte Beispiele

- x^{3} - 6 x^{2} - 8 x = 0

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

5 y^{4} - 15 y^{2} + 4 = 0

16x^3-48x^2-200=0

16 x^{3} - 48 x^{2} - 200 = 0

i z^{3} + 8 = 0