4x^3+9x^2+22x+5=0

Lösung

4 x^{3} + 9 x^{2} + 22 x + 5 = 0

x = - \frac{1}{4}, x = - 1 + 2 i, x = - 1 - 2 i

Schritte zur Lösung

4 x^{3} + 9 x^{2} + 22 x + 5 = 0

Faktorisiere

4 x^{3} + 9 x^{2} + 22 x + 5 : (4 x + 1) (x^{2} + 2 x + 5)

(4 x + 1) (x^{2} + 2 x + 5) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

4 x + 1 = 0 or x^{2} + 2 x + 5 = 0

Löse

4 x + 1 = 0 : x = - \frac{1}{4}

Löse

x^{2} + 2 x + 5 = 0 : x = - 1 + 2 i, x = - 1 - 2 i

Die Lösungen sind

x = - \frac{1}{4}, x = - 1 + 2 i, x = - 1 - 2 i

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

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

\frac{[ ( 13 + x ) ( 13 - x ) ( 3 + x ) ( 3 - x ) ]}{16} = 144

x^{5} - 3 x^{2} + x + 10 = 0

(x^{2} + x - 6)^{2} - (x^{2} + 2 x + 1)^{2} = 0