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Beliebt Algebra >

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

Lösung

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

Lösung

x = 0, x = 1, x = - 2, x = 2

+1

Dezimale

x = 0, x = 1, x = - 1.41421 \dots, x = 1.41421 \dots

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x - 1 = 0 or x + 2 = 0 or x - 2 = 0

Löse

x - 1 = 0 : x = 1

Löse

x + 2 = 0 : x = - 2

Löse

x - 2 = 0 : x = 2

Die Lösungen sind

x = 0, x = 1, x = - 2, x = 2

Graph

Beliebte Beispiele

3x^3+19x^2+21x+5=0

3 x^{3} + 19 x^{2} + 21 x + 5 = 0

3x^1-6x^2+7x^3=4

3 x^{1} - 6 x^{2} + 7 x^{3} = 4

a x^{5} + b = 0

s^{3} - 1 = 1

2x^3-x^2+18x-9=0

2 x^{3} - x^{2} + 18 x - 9 = 0