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Beliebt Algebra >

x^4+8x^3+8x^2+8x+7=0

Lösung

x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 7 = 0

Lösung

x = - 1, x = - 7, x = i, x = - i

Schritte zur Lösung

x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 7 = 0

Faktorisiere

x^{4} + 8 x^{3} + 8 x^{2} + 8 x + 7 : (x + 1) (x + 7) (x^{2} + 1)

(x + 1) (x + 7) (x^{2} + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or x + 7 = 0 or x^{2} + 1 = 0

Löse

x + 1 = 0 : x = - 1

Löse

x + 7 = 0 : x = - 7

Löse

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

Die Lösungen sind

x = - 1, x = - 7, x = i, x = - i

Graph

Beliebte Beispiele

240x^3+360x^2-1800x=0

240 x^{3} + 360 x^{2} - 1800 x = 0

wurzeln von x^3-2x^2+9x-18

roo t s x^{3} - 2 x^{2} + 9 x - 18

x^4-8x^3+26x^2-40x+25=0

x^{4} - 8 x^{3} + 26 x^{2} - 40 x + 25 = 0

2 x^{3} + 6 x - 1 = 0

w^{4} + 36 = 13 w^{2}