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Beliebt Algebra >

2x^5-x^3+2x^2-1=0

Lösung

2 x^{5} - x^{3} + 2 x^{2} - 1 = 0

Lösung

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

Schritte zur Lösung

2 x^{5} - x^{3} + 2 x^{2} - 1 = 0

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

2 x + 1 = 0 : x = - \frac{1}{2}

Löse

2 x - 1 = 0 : x = \frac{1}{2}

Löse

x + 1 = 0 : x = - 1

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

Graph

Beliebte Beispiele

5 x^{3} - 5 x = 0

k^{4} - 1 = 0

z^{4} + 4 i z^{2} + 8 = 0

x^{100} = 0

x^{5} = 4