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

Lösung

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

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

Schritte zur Lösung

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

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 3 = 0 : x = - 3

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

4 x^{3} + 12 x^{2} + 16 x = 0

x^{4} - 6 x^{3} + 6 x^{2} - 6 x + 5 = 0

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

so l v e f or z, (a) z^{4} = 24 i - 7

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