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Beliebt Algebra >

3x^3-7x^2+75x-175=0

Lösung

3 x^{3} - 7 x^{2} + 75 x - 175 = 0

Lösung

x = \frac{7}{3}, x = 5 i, x = - 5 i

Schritte zur Lösung

3 x^{3} - 7 x^{2} + 75 x - 175 = 0

Faktorisiere

3 x^{3} - 7 x^{2} + 75 x - 175 : (3 x - 7) (x^{2} + 25)

(3 x - 7) (x^{2} + 25) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

3 x - 7 = 0 or x^{2} + 25 = 0

Löse

3 x - 7 = 0 : x = \frac{7}{3}

Löse

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

Die Lösungen sind

x = \frac{7}{3}, x = 5 i, x = - 5 i

Graph

Beliebte Beispiele

x^3-4x^2+9x-36=0

x^{3} - 4 x^{2} + 9 x - 36 = 0

x^4-8x^3+24x^2-32x+16=0

x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16 = 0

x^4-4x^3+x^2-5x=3

x^{4} - 4 x^{3} + x^{2} - 5 x = 3

x^7-6x^5-x^2+x-7=0

x^{7} - 6 x^{5} - x^{2} + x - 7 = 0

2(x^2-100)(36x^2-49)=0

2 (x^{2} - 100) (36 x^{2} - 49) = 0