x^3+3x^2+2x-720=0

Lösung

x^{3} + 3 x^{2} + 2 x - 720 = 0

x = 8, x = - \frac{11}{2} + i \frac{239}{2}, x = - \frac{11}{2} - i \frac{239}{2}

Schritte zur Lösung

x^{3} + 3 x^{2} + 2 x - 720 = 0

Faktorisiere

x^{3} + 3 x^{2} + 2 x - 720 : (x - 8) (x^{2} + 11 x + 90)

(x - 8) (x^{2} + 11 x + 90) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 8 = 0 or x^{2} + 11 x + 90 = 0

Löse

x - 8 = 0 : x = 8

Löse

x^{2} + 11 x + 90 = 0 : x = - \frac{11}{2} + i \frac{239}{2}, x = - \frac{11}{2} - i \frac{239}{2}

Die Lösungen sind

x = 8, x = - \frac{11}{2} + i \frac{239}{2}, x = - \frac{11}{2} - i \frac{239}{2}

λ^{3} - 21 λ^{2} + 84 λ - 64 = 0

- x^{3} + x^{2} - 25 x + 25 = 0

x^{4} - 8 x^{2} - x + 12 = 0

15 x^{4} - 8 x^{3} + 54 x^{2} + 18 x - 4 = 0

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