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Beliebt Algebra >

-4x^5+32x^3+192x=0

Lösung

- 4 x^{5} + 32 x^{3} + 192 x = 0

Lösung

x = 0, x = 2 i, x = - 2 i, x = - 23, x = 23

Schritte zur Lösung

- 4 x^{5} + 32 x^{3} + 192 x = 0

Faktorisiere

- 4 x^{5} + 32 x^{3} + 192 x : - 4 x (x^{2} + 4) (x + 23) (x - 23)

- 4 x (x^{2} + 4) (x + 23) (x - 23) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x^{2} + 4 = 0 or x + 23 = 0 or x - 23 = 0

Löse

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

Löse

x + 23 = 0 : x = - 23

Löse

x - 23 = 0 : x = 23

Die Lösungen sind

x = 0, x = 2 i, x = - 2 i, x = - 23, x = 23

Graph

Beliebte Beispiele

-2x^3-x^2+8x-5=0

- 2 x^{3} - x^{2} + 8 x - 5 = 0

(x^{3}) (x + 3) = 5

x^3+6x^2-9x+4=0

x^{3} + 6 x^{2} - 9 x + 4 = 0

solvefor y,y^3=x^3-9x

so l v e f or y, y^{3} = x^{3} - 9 x

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