0=x^2-2x^3-10x+11

Lösung

0 = x^{2} - 2 x^{3} - 10 x + 11

x = 1, x = - \frac{1}{4} + i \frac{87}{4}, x = - \frac{1}{4} - i \frac{87}{4}

Schritte zur Lösung

0 = x^{2} - 2 x^{3} - 10 x + 11

Tausche die Seiten

x^{2} - 2 x^{3} - 10 x + 11 = 0

Schreibe in der Standard Form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 2 x^{3} + x^{2} - 10 x + 11 = 0

Faktorisiere

- 2 x^{3} + x^{2} - 10 x + 11 : - (x - 1) (2 x^{2} + x + 11)

- (x - 1) (2 x^{2} + x + 11) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 1 = 0 or 2 x^{2} + x + 11 = 0

Löse

x - 1 = 0 : x = 1

Löse

2 x^{2} + x + 11 = 0 : x = - \frac{1}{4} + i \frac{87}{4}, x = - \frac{1}{4} - i \frac{87}{4}

Die Lösungen sind

x = 1, x = - \frac{1}{4} + i \frac{87}{4}, x = - \frac{1}{4} - i \frac{87}{4}

3 x^{4} + 5 x^{3} - 11 x^{2} + 2 x - 3 = 0

x^{2} (x^{2} - 81) - 49 (x^{2} - 81) = 0

3 x^{3} - 5 x^{2} - 1 = 0

(x + 2)^{4} = 81

5 = 4 x^{3} + 12 x^{2} + 12 x + 4