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Beliebt Algebra >

2x^4-7x^3+21x^2+17x-13=0

Lösung

2 x^{4} - 7 x^{3} + 21 x^{2} + 17 x - 13 = 0

Lösung

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

Schritte zur Lösung

2 x^{4} - 7 x^{3} + 21 x^{2} + 17 x - 13 = 0

Faktorisiere

2 x^{4} - 7 x^{3} + 21 x^{2} + 17 x - 13 : (x + 1) (2 x - 1) (x^{2} - 4 x + 13)

(x + 1) (2 x - 1) (x^{2} - 4 x + 13) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or 2 x - 1 = 0 or x^{2} - 4 x + 13 = 0

Löse

x + 1 = 0 : x = - 1

Löse

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

Löse

x^{2} - 4 x + 13 = 0 : x = 2 + 3 i, x = 2 - 3 i

Die Lösungen sind

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

Graph

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