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Beliebt Algebra >

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

Lösung

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

Lösung

r = - 1, r = 1, r = 1 + i, r = 1 - i

Schritte zur Lösung

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

Faktorisiere

r^{4} - 2 r^{3} + r^{2} + 2 r - 2 : (r + 1) (r - 1) (r^{2} - 2 r + 2)

(r + 1) (r - 1) (r^{2} - 2 r + 2) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

r + 1 = 0 or r - 1 = 0 or r^{2} - 2 r + 2 = 0

Löse

r + 1 = 0 : r = - 1

Löse

r - 1 = 0 : r = 1

Löse

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

Die Lösungen sind

r = - 1, r = 1, r = 1 + i, r = 1 - i

Graph

Beliebte Beispiele

3 x^{3} - 81 = 0

x^3-594x+3186=0

x^{3} - 594 x + 3186 = 0

x^4-6x^3-3x^2+24x-4=0

x^{4} - 6 x^{3} - 3 x^{2} + 24 x - 4 = 0

x^{5} = x^{4}

faktorisieren x^3+3x^2-4x-12=0

f a c t or x^{3} + 3 x^{2} - 4 x - 12 = 0