x^4+14x^3+77x^2+200x+208=0

Lösung

x^{4} + 14 x^{3} + 77 x^{2} + 200 x + 208 = 0

x = - 4, x = - 3 + 2 i, x = - 3 - 2 i

Schritte zur Lösung

x^{4} + 14 x^{3} + 77 x^{2} + 200 x + 208 = 0

Faktorisiere

x^{4} + 14 x^{3} + 77 x^{2} + 200 x + 208 : (x + 4)^{2} (x^{2} + 6 x + 13)

(x + 4)^{2} (x^{2} + 6 x + 13) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 4 = 0 or x^{2} + 6 x + 13 = 0

Löse

x + 4 = 0 : x = - 4

Löse

x^{2} + 6 x + 13 = 0 : x = - 3 + 2 i, x = - 3 - 2 i

Die Lösungen sind

x = - 4, x = - 3 + 2 i, x = - 3 - 2 i

roo t s 2.5 x^{4} + 3 x^{3} - 2.6 x^{2} - 5.1 x - 5.6

x^{3} + 3 x^{2} - 14 x - 20 = 0

x^{3} - 16 x^{2} + 77 x - 98 = 0

3 x^{5} - 5 x^{4} + 2 x^{3} - x^{2} + 4 x - 1 = 0

x^{4} - 2.3 x^{3} + 4 = 4