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Beliebt Algebra >

2x^4+x^3-11x^2+x+2=0

Lösung

2 x^{4} + x^{3} - 11 x^{2} + x + 2 = 0

Lösung

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

+1

Dezimale

x = 2, x = 0.5, x = - 0.38196 \dots, x = - 2.61803 \dots

Schritte zur Lösung

2 x^{4} + x^{3} - 11 x^{2} + x + 2 = 0

Faktorisiere

2 x^{4} + x^{3} - 11 x^{2} + x + 2 : (x - 2) (2 x - 1) (x^{2} + 3 x + 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 2 = 0 : x = 2

Löse

2 x - 1 = 0 : x = \frac{1}{2}

Löse

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

Die Lösungen sind

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

Graph

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