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Beliebt Algebra >

x^4+7x^3+6x^2-22x+8=0

Lösung

x^{4} + 7 x^{3} + 6 x^{2} - 22 x + 8 = 0

Lösung

x = 1, x = - 4, x = - 2 + 6, x = - 2 - 6

+1

Dezimale

x = 1, x = - 4, x = 0.44948 \dots, x = - 4.44948 \dots

Schritte zur Lösung

x^{4} + 7 x^{3} + 6 x^{2} - 22 x + 8 = 0

Faktorisiere

x^{4} + 7 x^{3} + 6 x^{2} - 22 x + 8 : (x - 1) (x + 4) (x^{2} + 4 x - 2)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 1 = 0 : x = 1

Löse

x + 4 = 0 : x = - 4

Löse

x^{2} + 4 x - 2 = 0 : x = - 2 + 6, x = - 2 - 6

Die Lösungen sind

x = 1, x = - 4, x = - 2 + 6, x = - 2 - 6

Graph

Beliebte Beispiele

3(x-5)(x^2-2)=0

3 (x - 5) (x^{2} - 2) = 0

x^{4} - 4 x^{2} + 16 = 0

a^{4} = 625

3 x^{4} = 3000 x

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

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