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Beliebt Algebra >

x^4-3x^3-5x^2+13x+6=0

Lösung

x^{4} - 3 x^{3} - 5 x^{2} + 13 x + 6 = 0

Lösung

x = - 2, x = 3, x = 1 + 2, x = 1 - 2

+1

Dezimale

x = - 2, x = 3, x = 2.41421 \dots, x = - 0.41421 \dots

Schritte zur Lösung

x^{4} - 3 x^{3} - 5 x^{2} + 13 x + 6 = 0

Faktorisiere

x^{4} - 3 x^{3} - 5 x^{2} + 13 x + 6 : (x + 2) (x - 3) (x^{2} - 2 x - 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 2 = 0 : x = - 2

Löse

x - 3 = 0 : x = 3

Löse

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

Die Lösungen sind

x = - 2, x = 3, x = 1 + 2, x = 1 - 2

Graph

Beliebte Beispiele

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

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4 x^{3} + 30 x^{2} + 70 x + 50 = 0

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x^3-15x^2+72x-108=0

x^{3} - 15 x^{2} + 72 x - 108 = 0

2 x^{3} + 16 x^{2} = 0