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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

x^3-2x^2-6x+12=0

x^{3} - 2 x^{2} - 6 x + 12 = 0

x (x - 3) (x + 5) = 0

x^4+5x^3-16x^2+40x-192=0

x^{4} + 5 x^{3} - 16 x^{2} + 40 x - 192 = 0

y^{3} - y^{2} - 12 y = 0

2 x^{7} = 3 x^{9}