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Beliebt Algebra >

6x^5+11x^4-39x^3-41x^2+45x+18=0

Lösung

6 x^{5} + 11 x^{4} - 39 x^{3} - 41 x^{2} + 45 x + 18 = 0

Lösung

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

+1

Dezimale

x = 1, x = 2, x = - 3, x = - 0.33333 \dots, x = - 1.5

Schritte zur Lösung

6 x^{5} + 11 x^{4} - 39 x^{3} - 41 x^{2} + 45 x + 18 = 0

Faktorisiere

6 x^{5} + 11 x^{4} - 39 x^{3} - 41 x^{2} + 45 x + 18 : (x - 1) (x - 2) (x + 3) (3 x + 1) (2 x + 3)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 1 = 0 : x = 1

Löse

x - 2 = 0 : x = 2

Löse

x + 3 = 0 : x = - 3

Löse

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

Löse

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

Die Lösungen sind

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

Graph

Beliebte Beispiele

5 x^{3} = 320

wurzeln von x^3-2x^2+x-2

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

solvefor x,(x^2+y)^3=y

so l v e f or x, (x^{2} + y)^{3} = y

30x^3-113x^2+108x-30=0

30 x^{3} - 113 x^{2} + 108 x - 30 = 0

y^{4} - 12 y^{2} - 64 = 0