4w^4+8w^3-17w^2-21w-18=0

Lösung

4 w^{4} + 8 w^{3} - 17 w^{2} - 21 w - 18 = 0

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

Schritte zur Lösung

4 w^{4} + 8 w^{3} - 17 w^{2} - 21 w - 18 = 0

Faktorisiere

4 w^{4} + 8 w^{3} - 17 w^{2} - 21 w - 18 : (w - 2) (w + 3) (4 w^{2} + 4 w + 3)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

w - 2 = 0 or w + 3 = 0 or 4 w^{2} + 4 w + 3 = 0

Löse

w - 2 = 0 : w = 2

Löse

w + 3 = 0 : w = - 3

Löse

4 w^{2} + 4 w + 3 = 0 : w = - \frac{1}{2} + i \frac{2}{2}, w = - \frac{1}{2} - i \frac{2}{2}

Die Lösungen sind

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

2 x^{4} = 32

4 x^{4} + 4 x^{3} + x^{2} = 0

x^{4} - 15 x^{2} - 10 x + 24 = 0

20 x^{4} + 160 x^{2} - 285 = 0

59 = \frac{1}{4} (75 x - x^{3})