x^3+6x^2+12x+7=0

Lösung

x^{3} + 6 x^{2} + 12 x + 7 = 0

x = - 1, x = - \frac{5}{2} + i \frac{3}{2}, x = - \frac{5}{2} - i \frac{3}{2}

Schritte zur Lösung

x^{3} + 6 x^{2} + 12 x + 7 = 0

Faktorisiere

x^{3} + 6 x^{2} + 12 x + 7 : (x + 1) (x^{2} + 5 x + 7)

(x + 1) (x^{2} + 5 x + 7) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or x^{2} + 5 x + 7 = 0

Löse

x + 1 = 0 : x = - 1

Löse

x^{2} + 5 x + 7 = 0 : x = - \frac{5}{2} + i \frac{3}{2}, x = - \frac{5}{2} - i \frac{3}{2}

Die Lösungen sind

x = - 1, x = - \frac{5}{2} + i \frac{3}{2}, x = - \frac{5}{2} - i \frac{3}{2}

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

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

s^{5} + s^{4} + 4 s^{3} + 24 s^{2} + 3 s + 63 = 0

27 x^{5} - 54 x^{4} - 72 x^{3} - 26 x^{2} - 3 x = 0

roo t s 3 x^{4} - 7 x^{3} - 9 x^{2} + 24 x - 4