2x^3+6x^2+5x+2=0

Lösung

2 x^{3} + 6 x^{2} + 5 x + 2 = 0

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

Schritte zur Lösung

2 x^{3} + 6 x^{2} + 5 x + 2 = 0

Faktorisiere

2 x^{3} + 6 x^{2} + 5 x + 2 : (x + 2) (2 x^{2} + 2 x + 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 2 = 0 : x = - 2

Löse

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

Die Lösungen sind

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

4 x^{4} + 12 x^{3} + 5 x^{2} = 0

x^{4} - 6 x^{2} + 10 = 0

roo t s - 6 x^{3} - 48 x^{2} - 66 x + 120

x^{3} + 3 x^{2} - 7 x - 21 = 0

(x^{2} + 7)^{2} = 0