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Beliebt Algebra >

x^4+2x^3-6x^2+2x+1=0

Lösung

x^{4} + 2 x^{3} - 6 x^{2} + 2 x + 1 = 0

Lösung

x = 1, x = - 2 + 3, x = - 2 - 3

+1

Dezimale

x = 1, x = - 0.26794 \dots, x = - 3.73205 \dots

Schritte zur Lösung

x^{4} + 2 x^{3} - 6 x^{2} + 2 x + 1 = 0

Faktorisiere

x^{4} + 2 x^{3} - 6 x^{2} + 2 x + 1 : (x - 1)^{2} (x^{2} + 4 x + 1)

(x - 1)^{2} (x^{2} + 4 x + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 1 = 0 : x = 1

Löse

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

Die Lösungen sind

x = 1, x = - 2 + 3, x = - 2 - 3

Graph

Beliebte Beispiele

89=(5+x)(2x)(x)

89 = (5 + x) (2 x) (x)

-(4s^3+36s^2+128s+128)=0

- (4 s^{3} + 36 s^{2} + 128 s + 128) = 0

9 x^{4} + 4 x^{2} + 1 = 0

x^{4} = \frac{x}{2}

6 x^{3} + 14 = 0