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Beliebt Algebra >

x^4-2x^3+10x^2-20x=0

Lösung

x^{4} - 2 x^{3} + 10 x^{2} - 20 x = 0

Lösung

x = 0, x = 2, x = 10 i, x = - 10 i

Schritte zur Lösung

x^{4} - 2 x^{3} + 10 x^{2} - 20 x = 0

Faktorisiere

x^{4} - 2 x^{3} + 10 x^{2} - 20 x : x (x - 2) (x^{2} + 10)

x (x - 2) (x^{2} + 10) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x - 2 = 0 or x^{2} + 10 = 0

Löse

x - 2 = 0 : x = 2

Löse

x^{2} + 10 = 0 : x = 10 i, x = - 10 i

Die Lösungen sind

x = 0, x = 2, x = 10 i, x = - 10 i

Graph

Beliebte Beispiele

(2+h)^3-9(2)h=0.1

(2 + h)^{3} - 9 (2) h = 0.1

D^4+2D^3-11D^2-12D=0

D^{4} + 2 D^{3} - 11 D^{2} - 12 D = 0

solvefor x,x^3-y^5=0

so l v e f or x, x^{3} - y^{5} = 0

x^6+6x^4+9x^2+4=0

x^{6} + 6 x^{4} + 9 x^{2} + 4 = 0

y^{4} - 26 y^{2} + 25 = 0