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Beliebt Algebra >

(x-1)(x-2)(x^2-3x)=24

Lösung

(x - 1) (x - 2) (x^{2} - 3 x) = 24

Lösung

x = - 1, x = 4, x = \frac{3}{2} + i \frac{15}{2}, x = \frac{3}{2} - i \frac{15}{2}

Schritte zur Lösung

(x - 1) (x - 2) (x^{2} - 3 x) = 24

Schreibe

(x - 1) (x - 2) (x^{2} - 3 x)

um:

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

x^{4} - 6 x^{3} + 11 x^{2} - 6 x = 24

Verschiebe

24

auf die linke Seite

x^{4} - 6 x^{3} + 11 x^{2} - 6 x - 24 = 0

Faktorisiere

x^{4} - 6 x^{3} + 11 x^{2} - 6 x - 24 : (x + 1) (x - 4) (x^{2} - 3 x + 6)

(x + 1) (x - 4) (x^{2} - 3 x + 6) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 1 = 0 or x - 4 = 0 or x^{2} - 3 x + 6 = 0

Löse

x + 1 = 0 : x = - 1

Löse

x - 4 = 0 : x = 4

Löse

x^{2} - 3 x + 6 = 0 : x = \frac{3}{2} + i \frac{15}{2}, x = \frac{3}{2} - i \frac{15}{2}

Die Lösungen sind

x = - 1, x = 4, x = \frac{3}{2} + i \frac{15}{2}, x = \frac{3}{2} - i \frac{15}{2}

Graph

Beliebte Beispiele

x^{2} + 11 x^{24} = 0

- a^{3} - a^{2} - a = 3

(2 x + 1)^{4} = 81

x^{3} - 5 x^{2} = 36 x

81 = a^{4}