2x^4+5x^3+4-x^2=0

Lösung

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

x = - 1, x \approx - 2.57716 \dots

Schritte zur Lösung

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

Schreibe in der Standard Form

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

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

Faktorisiere

2 x^{4} + 5 x^{3} - x^{2} + 4 : (x + 1) (2 x^{3} + 3 x^{2} - 4 x + 4)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 1 = 0 : x = - 1

Löse

2 x^{3} + 3 x^{2} - 4 x + 4 = 0 : x \approx - 2.57716 \dots

Die Lösungen sind

x = - 1, x \approx - 2.57716 \dots

a^{10} = 15 a^{15}, a^{5} = 5

x^{3} - 9 x^{3} = 8

14 n^{3} - 2 n^{2} = 0

2 x^{4} + x^{3} - 29 x^{2} - 34 x = 24

- x^{3} + 9 x^{2} = 0