24x^5+10x^4-x^3-19x^2-5x+6=0

Lösung

24 x^{5} + 10 x^{4} - x^{3} - 19 x^{2} - 5 x + 6 = 0

x = \frac{1}{2}, x = - \frac{2}{3}, x = \frac{3}{4}, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Schritte zur Lösung

24 x^{5} + 10 x^{4} - x^{3} - 19 x^{2} - 5 x + 6 = 0

Faktorisiere

24 x^{5} + 10 x^{4} - x^{3} - 19 x^{2} - 5 x + 6 : (2 x - 1) (3 x + 2) (4 x - 3) (x^{2} + x + 1)

(2 x - 1) (3 x + 2) (4 x - 3) (x^{2} + x + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

2 x - 1 = 0 or 3 x + 2 = 0 or 4 x - 3 = 0 or x^{2} + x + 1 = 0

Löse

2 x - 1 = 0 : x = \frac{1}{2}

Löse

3 x + 2 = 0 : x = - \frac{2}{3}

Löse

4 x - 3 = 0 : x = \frac{3}{4}

Löse

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

Die Lösungen sind

x = \frac{1}{2}, x = - \frac{2}{3}, x = \frac{3}{4}, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}