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Beliebt Algebra >

x^4-5x^3+3x^2+x=0

Lösung

x^{4} - 5 x^{3} + 3 x^{2} + x = 0

Lösung

x = 0, x = 1, x = 2 + 5, x = 2 - 5

+1

Dezimale

x = 0, x = 1, x = 4.23606 \dots, x = - 0.23606 \dots

Schritte zur Lösung

x^{4} - 5 x^{3} + 3 x^{2} + x = 0

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 1 = 0 : x = 1

Löse

x^{2} - 4 x - 1 = 0 : x = 2 + 5, x = 2 - 5

Die Lösungen sind

x = 0, x = 1, x = 2 + 5, x = 2 - 5

Graph

Beliebte Beispiele

4 x^{4} - 65 x^{2} = 16

12x^3-12x^2-24x=0

12 x^{3} - 12 x^{2} - 24 x = 0

x^{4} + 5 x^{2} + 16 = 0

x^{3} + x^{2} - 18 = 0

x^{7} = x + 1