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Beliebt Algebra >

x^4-2x^3+x^2-8x-12=0

Lösung

x^{4} - 2 x^{3} + x^{2} - 8 x - 12 = 0

Lösung

x = - 1, x = 3, x = 2 i, x = - 2 i

Schritte zur Lösung

x^{4} - 2 x^{3} + x^{2} - 8 x - 12 = 0

Faktorisiere

x^{4} - 2 x^{3} + x^{2} - 8 x - 12 : (x + 1) (x - 3) (x^{2} + 4)

(x + 1) (x - 3) (x^{2} + 4) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or x - 3 = 0 or x^{2} + 4 = 0

Löse

x + 1 = 0 : x = - 1

Löse

x - 3 = 0 : x = 3

Löse

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

Die Lösungen sind

x = - 1, x = 3, x = 2 i, x = - 2 i

Graph

Beliebte Beispiele

2x^3+2x^2-3x-1=0

2 x^{3} + 2 x^{2} - 3 x - 1 = 0

12x^3-20x^2+11x-2=0

12 x^{3} - 20 x^{2} + 11 x - 2 = 0

0=3x^3-x^2-12x+4

0 = 3 x^{3} - x^{2} - 12 x + 4

z^5=16sqrt(3)+16i

z^{5} = 163 + 16 i

15 = k^{3}