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Beliebt Algebra >

24x^4+16x^3-3x-2=0

Lösung

24 x^{4} + 16 x^{3} - 3 x - 2 = 0

Lösung

x = - \frac{2}{3}, x = \frac{1}{2}, x = - \frac{1}{4} + i \frac{3}{4}, x = - \frac{1}{4} - i \frac{3}{4}

Schritte zur Lösung

24 x^{4} + 16 x^{3} - 3 x - 2 = 0

Faktorisiere

24 x^{4} + 16 x^{3} - 3 x - 2 : (3 x + 2) (2 x - 1) (4 x^{2} + 2 x + 1)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

3 x + 2 = 0 : x = - \frac{2}{3}

Löse

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

Löse

4 x^{2} + 2 x + 1 = 0 : x = - \frac{1}{4} + i \frac{3}{4}, x = - \frac{1}{4} - i \frac{3}{4}

Die Lösungen sind

x = - \frac{2}{3}, x = \frac{1}{2}, x = - \frac{1}{4} + i \frac{3}{4}, x = - \frac{1}{4} - i \frac{3}{4}

Graph

Beliebte Beispiele

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

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

x^{4} x + 8 = 8 x + 16

2x^5-12x^3=-16x

2 x^{5} - 12 x^{3} = - 16 x

-λ^3-13λ^2-56λ-80=0

- λ^{3} - 13 λ^{2} - 56 λ - 80 = 0

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