x^3+x^2-12=0

Lösung

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

x = 2, x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

Schritte zur Lösung

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

Faktorisiere

x^{3} + x^{2} - 12 : (x - 2) (x^{2} + 3 x + 6)

(x - 2) (x^{2} + 3 x + 6) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 2 = 0 : x = 2

Löse

x^{2} + 3 x + 6 = 0 : x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

Die Lösungen sind

x = 2, x = - \frac{3}{2} + i \frac{15}{2}, x = - \frac{3}{2} - i \frac{15}{2}

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

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