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Beliebt Algebra >

x^4+7x^3-2x^2-7x+1=0

Lösung

x^{4} + 7 x^{3} - 2 x^{2} - 7 x + 1 = 0

Lösung

x = - 1, x = 1, x = \frac{- 7 + 53}{2}, x = \frac{- 7 - 53}{2}

+1

Dezimale

x = - 1, x = 1, x = 0.14005 \dots, x = - 7.14005 \dots

Schritte zur Lösung

x^{4} + 7 x^{3} - 2 x^{2} - 7 x + 1 = 0

Faktorisiere

x^{4} + 7 x^{3} - 2 x^{2} - 7 x + 1 : (x + 1) (x - 1) (x^{2} + 7 x - 1)

(x + 1) (x - 1) (x^{2} + 7 x - 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or x - 1 = 0 or x^{2} + 7 x - 1 = 0

Löse

x + 1 = 0 : x = - 1

Löse

x - 1 = 0 : x = 1

Löse

x^{2} + 7 x - 1 = 0 : x = \frac{- 7 + 53}{2}, x = \frac{- 7 - 53}{2}

Die Lösungen sind

x = - 1, x = 1, x = \frac{- 7 + 53}{2}, x = \frac{- 7 - 53}{2}

Graph

Beliebte Beispiele

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

x^3+7x^2+9x+63=0

x^{3} + 7 x^{2} + 9 x + 63 = 0

(x^{3} - 8) = 0

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

solvefor x,(x+y)^5=3

so l v e f or x, (x + y)^{5} = 3