2x^4-3x^3-7x^2-8x+6=0

Lösung

2 x^{4} - 3 x^{3} - 7 x^{2} - 8 x + 6 = 0

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

Schritte zur Lösung

2 x^{4} - 3 x^{3} - 7 x^{2} - 8 x + 6 = 0

Faktorisiere

2 x^{4} - 3 x^{3} - 7 x^{2} - 8 x + 6 : (x - 3) (2 x - 1) (x^{2} + 2 x + 2)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 3 = 0 : x = 3

Löse

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

Löse

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

Die Lösungen sind

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

- 3 x^{3} + 4 x^{2} - 12 x + 16 = 0

a^{3} + 3 a^{2} + 2 a = 0

2 y^{2} - 2 y = 12 y^{2} - 12 y^{3}

4 x^{3} - 28 x - 24 = 0

roo t s x^{3} + 9 x^{2} + 20 x = 0