25x^2+8x^3-441=0

Lösung

25 x^{2} + 8 x^{3} - 441 = 0

x = 3, x = - \frac{49}{16} + i \frac{7 47}{16}, x = - \frac{49}{16} - i \frac{7 47}{16}

Schritte zur Lösung

25 x^{2} + 8 x^{3} - 441 = 0

Schreibe in der Standard Form

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

8 x^{3} + 25 x^{2} - 441 = 0

Faktorisiere

8 x^{3} + 25 x^{2} - 441 : (x - 3) (8 x^{2} + 49 x + 147)

(x - 3) (8 x^{2} + 49 x + 147) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 3 = 0 or 8 x^{2} + 49 x + 147 = 0

Löse

x - 3 = 0 : x = 3

Löse

8 x^{2} + 49 x + 147 = 0 : x = - \frac{49}{16} + i \frac{7 47}{16}, x = - \frac{49}{16} - i \frac{7 47}{16}

Die Lösungen sind

x = 3, x = - \frac{49}{16} + i \frac{7 47}{16}, x = - \frac{49}{16} - i \frac{7 47}{16}

3 x^{3} - 5 x + 5 = 0

- a^{3} + 4 a^{2} - 5 a + 2 = 0

x^{5} - x^{4} - 9 x^{3} = 0

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

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