2x^4-7x^3+12x^2-8x-8=0

Lösung

2 x^{4} - 7 x^{3} + 12 x^{2} - 8 x - 8 = 0

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

Schritte zur Lösung

2 x^{4} - 7 x^{3} + 12 x^{2} - 8 x - 8 = 0

Faktorisiere

2 x^{4} - 7 x^{3} + 12 x^{2} - 8 x - 8 : (x - 2) (2 x + 1) (x^{2} - 2 x + 4)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 2 = 0 : x = 2

Löse

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

Löse

x^{2} - 2 x + 4 = 0 : x = 1 + 3 i, x = 1 - 3 i

Die Lösungen sind

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

6 (- y + 4) - 3 (2 y - 3) = - y + 5 + 5 y

f a c t or 3 m^{2} + 6 m + 3

s im pl i f y x^{3} (x^{2})

f a c t or 9 w^{2} - 64

2 x - 8 < 12