2x^3-x^2-12=0

Lösung

2 x^{3} - x^{2} - 12 = 0

x = 2, x = - \frac{3}{4} + i \frac{39}{4}, x = - \frac{3}{4} - i \frac{39}{4}

Schritte zur Lösung

2 x^{3} - x^{2} - 12 = 0

Faktorisiere

2 x^{3} - x^{2} - 12 : (x - 2) (2 x^{2} + 3 x + 6)

(x - 2) (2 x^{2} + 3 x + 6) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 2 = 0 or 2 x^{2} + 3 x + 6 = 0

Löse

x - 2 = 0 : x = 2

Löse

2 x^{2} + 3 x + 6 = 0 : x = - \frac{3}{4} + i \frac{39}{4}, x = - \frac{3}{4} - i \frac{39}{4}

Die Lösungen sind

x = 2, x = - \frac{3}{4} + i \frac{39}{4}, x = - \frac{3}{4} - i \frac{39}{4}

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

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

(x^{2} - 1) \cdot (5 - x) = 0

(x^{2} + 2 x)^{2} - 5 (x^{2} + 2 x) + 6 = 0

so l v e f or a, a^{4} b + 2 c^{5} = d^{1} e