2.5x^4+3x^3-2.6x^2-5.1x-5.6=0

Lösung

2.5 x^{4} + 3 x^{3} - 2.6 x^{2} - 5.1 x - 5.6 = 0

x = \frac{7}{5}, x = - \frac{8}{5}, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Schritte zur Lösung

2.5 x^{4} + 3 x^{3} - 2.6 x^{2} - 5.1 x - 5.6 = 0

Multipliziere beide Seiten mit

10

25 x^{4} + 30 x^{3} - 26 x^{2} - 51 x - 56 = 0

Faktorisiere

25 x^{4} + 30 x^{3} - 26 x^{2} - 51 x - 56 : (5 x - 7) (5 x + 8) (x^{2} + x + 1)

(5 x - 7) (5 x + 8) (x^{2} + x + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

5 x - 7 = 0 or 5 x + 8 = 0 or x^{2} + x + 1 = 0

Löse

5 x - 7 = 0 : x = \frac{7}{5}

Löse

5 x + 8 = 0 : x = - \frac{8}{5}

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{7}{5}, x = - \frac{8}{5}, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}