x^3-4x^2-3x-10=0

Lösung

x^{3} - 4 x^{2} - 3 x - 10 = 0

x = 5, x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

Schritte zur Lösung

x^{3} - 4 x^{2} - 3 x - 10 = 0

Faktorisiere

x^{3} - 4 x^{2} - 3 x - 10 : (x - 5) (x^{2} + x + 2)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 5 = 0 or x^{2} + x + 2 = 0

Löse

x - 5 = 0 : x = 5

Löse

x^{2} + x + 2 = 0 : x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

Die Lösungen sind

x = 5, x = - \frac{1}{2} + i \frac{7}{2}, x = - \frac{1}{2} - i \frac{7}{2}

- x^{4} + 2 x^{2} + 8 = 0

x^{4} - 18 x^{3} + 103 x^{2} + 214 x + 192 = 0

so l v e f or x, x^{5} + y^{4} = 500

so l v e f or h, [h^{3} o] = 1.1 \cdot 1 0^{- 1} 3

x^{3} = - 216