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Beliebt Algebra >

x^4-5x^2-10x-6=0

Lösung

x^{4} - 5 x^{2} - 10 x - 6 = 0

Lösung

x = - 1, x = 3, x = - 1 + i, x = - 1 - i

Schritte zur Lösung

x^{4} - 5 x^{2} - 10 x - 6 = 0

Faktorisiere

x^{4} - 5 x^{2} - 10 x - 6 : (x + 1) (x - 3) (x^{2} + 2 x + 2)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 1 = 0 : x = - 1

Löse

x - 3 = 0 : x = 3

Löse

x^{2} + 2 x + 2 = 0 : x = - 1 + i, x = - 1 - i

Die Lösungen sind

x = - 1, x = 3, x = - 1 + i, x = - 1 - i

Graph

Beliebte Beispiele

100x^3-45x^2-58x+24=0

100 x^{3} - 45 x^{2} - 58 x + 24 = 0

9z^3+13z-2022=0

9 z^{3} + 13 z - 2022 = 0

x^{2} (x - 3) = 12 - 4 x

x^6+x^4-2x^3-2x+1=0

x^{6} + x^{4} - 2 x^{3} - 2 x + 1 = 0

-λ^3-λ^2+8λ+12=0

- λ^{3} - λ^{2} + 8 λ + 12 = 0