3x^3+2x^2-19x+6=0

Lösung

3 x^{3} + 2 x^{2} - 19 x + 6 = 0

x = 2, x = \frac{1}{3}, x = - 3

Dezimale

x = 2, x = 0.33333 \dots, x = - 3

Schritte zur Lösung

3 x^{3} + 2 x^{2} - 19 x + 6 = 0

Faktorisiere

3 x^{3} + 2 x^{2} - 19 x + 6 : (x - 2) (3 x - 1) (x + 3)

(x - 2) (3 x - 1) (x + 3) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 2 = 0 or 3 x - 1 = 0 or x + 3 = 0

Löse

x - 2 = 0 : x = 2

Löse

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

Löse

x + 3 = 0 : x = - 3

Die Lösungen sind

x = 2, x = \frac{1}{3}, x = - 3

r a t i o na l roo t s t es t x^{3} - 3 x^{2} - 25 x + 75 = 0

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

roo t s x^{3} - 2 x^{2} - 11 x + 12

x^{4} + 9 x^{3} + 12 x^{2} - 34 x + 12 = 0

r^{4} - 2 r^{3} + r^{2} + 2 r - 2 = 0