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Beliebt Algebra >

x^4+x^3+x+1=0

Lösung

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

Lösung

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

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

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

Graph

Beliebte Beispiele

6 x^{5} - 6 x^{4} = 0

895 = 5 x^{3}

3x^3-4x^2-35x+12=0

3 x^{3} - 4 x^{2} - 35 x + 12 = 0

18 x^{2} + 5 x = 8 x^{3}

solvefor x,1.21x^{10}=x+2

so l v e f or x, 1.21 x^{10} = x + 2