5x^3-27x^2-17x-6=0

Lösung

5 x^{3} - 27 x^{2} - 17 x - 6 = 0

x = 6, x = - \frac{3}{10} + i \frac{11}{10}, x = - \frac{3}{10} - i \frac{11}{10}

Schritte zur Lösung

5 x^{3} - 27 x^{2} - 17 x - 6 = 0

Faktorisiere

5 x^{3} - 27 x^{2} - 17 x - 6 : (x - 6) (5 x^{2} + 3 x + 1)

(x - 6) (5 x^{2} + 3 x + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 6 = 0 or 5 x^{2} + 3 x + 1 = 0

Löse

x - 6 = 0 : x = 6

Löse

5 x^{2} + 3 x + 1 = 0 : x = - \frac{3}{10} + i \frac{11}{10}, x = - \frac{3}{10} - i \frac{11}{10}

Die Lösungen sind

x = 6, x = - \frac{3}{10} + i \frac{11}{10}, x = - \frac{3}{10} - i \frac{11}{10}

5 x^{5} - 45 x = 0

- x^{4} - 8 x^{3} + 7 x^{2} + 56 x = 0

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

- λ^{3} + 5 λ^{2} - 3 λ - 9 = 0

200 x^{3} + 2000 x - 1000 = 0