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Beliebt Algebra >

x^4+x^3-4x^2+x+1=0

Lösung

x^{4} + x^{3} - 4 x^{2} + x + 1 = 0

Lösung

x = 1, x = \frac{- 3 + 5}{2}, x = \frac{- 3 - 5}{2}

+1

Dezimale

x = 1, x = - 0.38196 \dots, x = - 2.61803 \dots

Schritte zur Lösung

x^{4} + x^{3} - 4 x^{2} + x + 1 = 0

Faktorisiere

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

(x - 1)^{2} (x^{2} + 3 x + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 1 = 0 : x = 1

Löse

x^{2} + 3 x + 1 = 0 : x = \frac{- 3 + 5}{2}, x = \frac{- 3 - 5}{2}

Die Lösungen sind

x = 1, x = \frac{- 3 + 5}{2}, x = \frac{- 3 - 5}{2}

Graph

Beliebte Beispiele

x^{3} = 4

t^{16}-2t=t+9+4t

t^{16} - 2 t = t + 9 + 4 t

x^3-11x^2+36x-36=0

x^{3} - 11 x^{2} + 36 x - 36 = 0

x^{5} + x^{4} + 1 = 0

y^{3} + 1 = 0