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Beliebt Algebra >

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

Lösung

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

Lösung

x = - 1, x = 2, x = \frac{1}{2} + i \frac{7}{2}, x = \frac{1}{2} - i \frac{7}{2}

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 1 = 0 : x = - 1

Löse

x - 2 = 0 : x = 2

Löse

x^{2} - x + 2 = 0 : x = \frac{1}{2} + i \frac{7}{2}, x = \frac{1}{2} - i \frac{7}{2}

Die Lösungen sind

x = - 1, x = 2, x = \frac{1}{2} + i \frac{7}{2}, x = \frac{1}{2} - i \frac{7}{2}

Graph

Beliebte Beispiele

x = x^{5} + 5 x^{3} + 3

9a^3-81a=-2a^2+18

9 a^{3} - 81 a = - 2 a^{2} + 18

solvefor x,175=5x^3

so l v e f or x, 175 = 5 x^{3}

3 + 9 x^{8} - 6^{2} = A

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