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Beliebt Algebra >

2x^5-7x^4+12x^3+8x^2=0

Lösung

2 x^{5} - 7 x^{4} + 12 x^{3} + 8 x^{2} = 0

Lösung

x = 0, x = - \frac{1}{2}, x = 2 + 2 i, x = 2 - 2 i

Schritte zur Lösung

2 x^{5} - 7 x^{4} + 12 x^{3} + 8 x^{2} = 0

Faktorisiere

2 x^{5} - 7 x^{4} + 12 x^{3} + 8 x^{2} : x^{2} (2 x + 1) (x^{2} - 4 x + 8)

x^{2} (2 x + 1) (x^{2} - 4 x + 8) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or 2 x + 1 = 0 or x^{2} - 4 x + 8 = 0

Löse

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

Löse

x^{2} - 4 x + 8 = 0 : x = 2 + 2 i, x = 2 - 2 i

Die Lösungen sind

x = 0, x = - \frac{1}{2}, x = 2 + 2 i, x = 2 - 2 i

Graph

Beliebte Beispiele

x^{3} - 3 = 0

x^{4} - 2 x = 0

solvefor m,n=m^4

so l v e f or m, n = m^{4}

x^{3} + i = 0

solvefor F,d-F^3=4a

so l v e f or F, d - F^{3} = 4 a