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Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 2 = 0 : x = - 2

Löse

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

Graph

Beliebte Beispiele

y^{8} + 5 = - 3

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

x^3-7x^2+25x-39=0

x^{3} - 7 x^{2} + 25 x - 39 = 0

2x^3+16=x^2+32x

2 x^{3} + 16 = x^{2} + 32 x

2b^3+5=2(3)^3+5

2 b^{3} + 5 = 2 (3)^{3} + 5