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Beliebt Algebra >

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

Lösung

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

Lösung

x = 2, x = - 3, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Schritte zur Lösung

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

Faktorisiere

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

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

Löse

x - 2 = 0 : x = 2

Löse

x + 3 = 0 : x = - 3

Löse

x^{2} + x + 1 = 0 : x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Die Lösungen sind

x = 2, x = - 3, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Graph

Beliebte Beispiele

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

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

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

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4 x^{3} - 15 x^{2} + 18 x = 0

3 x^{4} - 75 x^{2} = 0

(5-x)*(x^2-9)=0

(5 - x) \cdot (x^{2} - 9) = 0