x^3+3x^2-112=0

Lösung

x^{3} + 3 x^{2} - 112 = 0

x = 4, x = - \frac{7}{2} + i \frac{3 7}{2}, x = - \frac{7}{2} - i \frac{3 7}{2}

Schritte zur Lösung

x^{3} + 3 x^{2} - 112 = 0

Faktorisiere

x^{3} + 3 x^{2} - 112 : (x - 4) (x^{2} + 7 x + 28)

(x - 4) (x^{2} + 7 x + 28) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 4 = 0 or x^{2} + 7 x + 28 = 0

Löse

x - 4 = 0 : x = 4

Löse

x^{2} + 7 x + 28 = 0 : x = - \frac{7}{2} + i \frac{3 7}{2}, x = - \frac{7}{2} - i \frac{3 7}{2}

Die Lösungen sind

x = 4, x = - \frac{7}{2} + i \frac{3 7}{2}, x = - \frac{7}{2} - i \frac{3 7}{2}

x^{4} - \frac{6}{7} x^{2} + \frac{3}{35} = 0

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

5 x^{4} + 7 x^{2} - 12 = 0

roo t s x^{3} + 4 x^{2} + x - 6

x^{4} - 3 x^{3} - 13 x^{2} + 9 x + 30 = 0