27x^5-54x^4-72x^3-26x^2-3x=0

Lösung

27 x^{5} - 54 x^{4} - 72 x^{3} - 26 x^{2} - 3 x = 0

x = 0, x = 3, x = - \frac{1}{3}

Dezimale

x = 0, x = 3, x = - 0.33333 \dots

Schritte zur Lösung

27 x^{5} - 54 x^{4} - 72 x^{3} - 26 x^{2} - 3 x = 0

Faktorisiere

27 x^{5} - 54 x^{4} - 72 x^{3} - 26 x^{2} - 3 x : x (x - 3) (3 x + 1)^{3}

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or x - 3 = 0 or 3 x + 1 = 0

Löse

x - 3 = 0 : x = 3

Löse

3 x + 1 = 0 : x = - \frac{1}{3}

Die Lösungen sind

x = 0, x = 3, x = - \frac{1}{3}

roo t s 3 x^{4} - 7 x^{3} - 9 x^{2} + 24 x - 4

2 x^{3} - 8 x^{2} + x - 4 = 0

roo t s 4 x^{3} - 12 x^{2}

3 x^{3} + 5 x^{2} + 75 x + 125 = 0

x^{4} - 4 x^{3} - x^{2} + 14 x + 10 = 0