x^3-5/6 x^2+35/6 x+1=0

Lösung

x^{3} - \frac{5}{6} x^{2} + \frac{35}{6} x + 1 = 0

x = - \frac{1}{6}, x = \frac{1}{2} + i \frac{23}{2}, x = \frac{1}{2} - i \frac{23}{2}

Schritte zur Lösung

x^{3} - \frac{5}{6} x^{2} + \frac{35}{6} x + 1 = 0

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6

6 x^{3} - 5 x^{2} + 35 x + 6 = 0

Faktorisiere

6 x^{3} - 5 x^{2} + 35 x + 6 : (6 x + 1) (x^{2} - x + 6)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

6 x + 1 = 0 : x = - \frac{1}{6}

Löse

x^{2} - x + 6 = 0 : x = \frac{1}{2} + i \frac{23}{2}, x = \frac{1}{2} - i \frac{23}{2}

Die Lösungen sind

x = - \frac{1}{6}, x = \frac{1}{2} + i \frac{23}{2}, x = \frac{1}{2} - i \frac{23}{2}

z^{12} = 1

x^{3} - 14 x^{2} + 12 x + 12 = 0

2 (x^{3} + 3 x^{2} + 12 x + 4) = 0

x^{4} - x^{2} + 9 = 0

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