x^5-7x^4+14x^3-2x^2-15x+9=0

Lösung

x^{5} - 7 x^{4} + 14 x^{3} - 2 x^{2} - 15 x + 9 = 0

x = - 1, x = 1, x = 3

Schritte zur Lösung

x^{5} - 7 x^{4} + 14 x^{3} - 2 x^{2} - 15 x + 9 = 0

Faktorisiere

x^{5} - 7 x^{4} + 14 x^{3} - 2 x^{2} - 15 x + 9 : (x + 1) (x - 1)^{2} (x - 3)^{2}

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or x - 1 = 0 or x - 3 = 0

Löse

x + 1 = 0 : x = - 1

Löse

x - 1 = 0 : x = 1

Löse

x - 3 = 0 : x = 3

Die Lösungen sind

x = - 1, x = 1, x = 3

r a t i o na l roo t s t es t x^{4} - 4 x^{3} - x^{2} + 14 x + 10

roo t s x^{4} + x^{2} + 1

x^{3} - 2 x^{2} - 11 x - 12 = 0

z^{6} - (3 + 2 i) z^{3} + 2 + 2 i = 0

roo t s x^{3} - 3 x^{2} - 10 x + 24