6x^4-x^3-6x^2-12x-5=0

Lösung

6 x^{4} - x^{3} - 6 x^{2} - 12 x - 5 = 0

x = - \frac{1}{2}, x = \frac{5}{3}, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Schritte zur Lösung

6 x^{4} - x^{3} - 6 x^{2} - 12 x - 5 = 0

Faktorisiere

6 x^{4} - x^{3} - 6 x^{2} - 12 x - 5 : (2 x + 1) (3 x - 5) (x^{2} + x + 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

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

Löse

3 x - 5 = 0 : x = \frac{5}{3}

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{5}{3}, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

((x + 3) (x - 3))^{2} = 100

c^{3} = - 64

x^{4} + 6 x^{3} + 3 x^{2} - 16 x + 6 = 0

- x^{3} - 6 x^{2} - 12 x - 8 = 0

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