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Beliebt Algebra >

x^4-5x^3+10x^2-16=0

Lösung

x^{4} - 5 x^{3} + 10 x^{2} - 16 = 0

Lösung

x = - 1, x = 2, x = 2 + 2 i, x = 2 - 2 i

Schritte zur Lösung

x^{4} - 5 x^{3} + 10 x^{2} - 16 = 0

Faktorisiere

x^{4} - 5 x^{3} + 10 x^{2} - 16 : (x + 1) (x - 2) (x^{2} - 4 x + 8)

(x + 1) (x - 2) (x^{2} - 4 x + 8) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or x - 2 = 0 or x^{2} - 4 x + 8 = 0

Löse

x + 1 = 0 : x = - 1

Löse

x - 2 = 0 : x = 2

Löse

x^{2} - 4 x + 8 = 0 : x = 2 + 2 i, x = 2 - 2 i

Die Lösungen sind

x = - 1, x = 2, x = 2 + 2 i, x = 2 - 2 i

Graph

Beliebte Beispiele

x^{4} = 8 x^{2} + 9

x^{3} + 2 x = 10

x^3+2x^2-21x+18=0

x^{3} + 2 x^{2} - 21 x + 18 = 0

4x^4-29x^2+25=0

4 x^{4} - 29 x^{2} + 25 = 0

5=(6x(x^3-1)^3)

5 = (6 x (x^{3} - 1)^{3})