4x^3-6x^2+4x-1=0

Lösung

4 x^{3} - 6 x^{2} + 4 x - 1 = 0

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

Schritte zur Lösung

4 x^{3} - 6 x^{2} + 4 x - 1 = 0

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

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

Löse

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

Die Lösungen sind

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

x^{4} - x^{2} - 20 = 0

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

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

- x^{3} + 7 x^{2} - 14 x + 8 = 0

4.5 t^{4} + 3.2 t^{3} + 25 t = 20