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Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 3 = 0 : x = 3

Löse

x + 1 = 0 : x = - 1

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

y^{3} + 27 = 0

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

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0 = 2 x^{9} - 3 x^{7} + 11 x + 10

x^{3} - 4 x^{2} + 1 = 0