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Beliebt Algebra >

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

Lösung

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

Lösung

x = - \frac{5}{3}, x = 5 i, x = - 5 i

Schritte zur Lösung

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

Faktorisiere

3 x^{3} + 5 x^{2} + 75 x + 125 : (3 x + 5) (x^{2} + 25)

(3 x + 5) (x^{2} + 25) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

3 x + 5 = 0 or x^{2} + 25 = 0

Löse

3 x + 5 = 0 : x = - \frac{5}{3}

Löse

x^{2} + 25 = 0 : x = 5 i, x = - 5 i

Die Lösungen sind

x = - \frac{5}{3}, x = 5 i, x = - 5 i

Graph

Beliebte Beispiele

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

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

x^3+8x^2+12x+18=0

x^{3} + 8 x^{2} + 12 x + 18 = 0

x^3+12x^2+32x=0

x^{3} + 12 x^{2} + 32 x = 0

solvefor x,x^3-7x^2=7-x

so l v e f or x, x^{3} - 7 x^{2} = 7 - x

x^4-4x^3+4x^2-36x-45=0

x^{4} - 4 x^{3} + 4 x^{2} - 36 x - 45 = 0