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Beliebt Algebra >

x^4+8x^3+14x^2-17x-42=0

Lösung

x^{4} + 8 x^{3} + 14 x^{2} - 17 x - 42 = 0

Lösung

x = - 2, x = - 3, x = \frac{- 3 + 37}{2}, x = \frac{- 3 - 37}{2}

+1

Dezimale

x = - 2, x = - 3, x = 1.54138 \dots, x = - 4.54138 \dots

Schritte zur Lösung

x^{4} + 8 x^{3} + 14 x^{2} - 17 x - 42 = 0

Faktorisiere

x^{4} + 8 x^{3} + 14 x^{2} - 17 x - 42 : (x + 2) (x + 3) (x^{2} + 3 x - 7)

(x + 2) (x + 3) (x^{2} + 3 x - 7) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 2 = 0 or x + 3 = 0 or x^{2} + 3 x - 7 = 0

Löse

x + 2 = 0 : x = - 2

Löse

x + 3 = 0 : x = - 3

Löse

x^{2} + 3 x - 7 = 0 : x = \frac{- 3 + 37}{2}, x = \frac{- 3 - 37}{2}

Die Lösungen sind

x = - 2, x = - 3, x = \frac{- 3 + 37}{2}, x = \frac{- 3 - 37}{2}

Graph

Beliebte Beispiele

2x^3+5x^2-13x+7=0

20x^3+12x^2-5x-3=0