de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

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

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

Graph

Beliebte Beispiele

\frac{1}{2 a} = n^{3}

x^{4} + x^{3} - x - 1 = 0

2-15x+9x^2-x^3=0

2 - 15 x + 9 x^{2} - x^{3} = 0

x^4+2x^3=x^2+2x

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

x (9 + x) (x - 2) = 4