x^4+17x^3+60x^2-59x+77=0

Lösung

x^{4} + 17 x^{3} + 60 x^{2} - 59 x + 77 = 0

x = - 7, x = - 11, x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}

Schritte zur Lösung

x^{4} + 17 x^{3} + 60 x^{2} - 59 x + 77 = 0

Faktorisiere

x^{4} + 17 x^{3} + 60 x^{2} - 59 x + 77 : (x + 7) (x + 11) (x^{2} - x + 1)

(x + 7) (x + 11) (x^{2} - x + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 7 = 0 or x + 11 = 0 or x^{2} - x + 1 = 0

Löse

x + 7 = 0 : x = - 7

Löse

x + 11 = 0 : x = - 11

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 = - 7, x = - 11, x = \frac{1}{2} + i \frac{3}{2}, x = \frac{1}{2} - i \frac{3}{2}

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

y^{4} - 1 = 0

- x^{3} + x^{2} + 17 x + 15 = 0

x^{3} = x^{2} - 7 x + 7

n^{3} + 2 n^{2} - 9 n - 18 = 0