6x^4+5x^3+25x^2+20x+4=0

Lösung

6 x^{4} + 5 x^{3} + 25 x^{2} + 20 x + 4 = 0

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

Schritte zur Lösung

6 x^{4} + 5 x^{3} + 25 x^{2} + 20 x + 4 = 0

Faktorisiere

6 x^{4} + 5 x^{3} + 25 x^{2} + 20 x + 4 : (2 x + 1) (3 x + 1) (x^{2} + 4)

(2 x + 1) (3 x + 1) (x^{2} + 4) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

2 x + 1 = 0 or 3 x + 1 = 0 or x^{2} + 4 = 0

Löse

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

Löse

3 x + 1 = 0 : x = - \frac{1}{3}

Löse

x^{2} + 4 = 0 : x = 2 i, x = - 2 i

Die Lösungen sind

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

x^{3} - 2 x^{2} + 62 - 0.5 = 0

f a c t or x^{4} + 2 x^{2} + 1 = 0

x^{4} - x^{3} + 7 x^{2} - 9 x - 18 = 0

3 y^{3} - 11 y^{2} - 4 y = 0

4 x^{3} - 36 x^{2} + 104 x - 96 = 0