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Beliebt Algebra >

x(x+1)(x+2)(x+3)=120

Lösung

x (x + 1) (x + 2) (x + 3) = 120

Lösung

x = 2, x = - 5, x = - \frac{3}{2} + i \frac{39}{2}, x = - \frac{3}{2} - i \frac{39}{2}

Schritte zur Lösung

x (x + 1) (x + 2) (x + 3) = 120

Schreibe

x (x + 1) (x + 2) (x + 3)

um:

x^{4} + 6 x^{3} + 11 x^{2} + 6 x

x^{4} + 6 x^{3} + 11 x^{2} + 6 x = 120

Verschiebe

120

auf die linke Seite

x^{4} + 6 x^{3} + 11 x^{2} + 6 x - 120 = 0

Faktorisiere

x^{4} + 6 x^{3} + 11 x^{2} + 6 x - 120 : (x - 2) (x + 5) (x^{2} + 3 x + 12)

(x - 2) (x + 5) (x^{2} + 3 x + 12) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 2 = 0 or x + 5 = 0 or x^{2} + 3 x + 12 = 0

Löse

x - 2 = 0 : x = 2

Löse

x + 5 = 0 : x = - 5

Löse

x^{2} + 3 x + 12 = 0 : x = - \frac{3}{2} + i \frac{39}{2}, x = - \frac{3}{2} - i \frac{39}{2}

Die Lösungen sind

x = 2, x = - 5, x = - \frac{3}{2} + i \frac{39}{2}, x = - \frac{3}{2} - i \frac{39}{2}

Graph

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