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Beliebt Algebra >

16x(x+1)(x+2)(x+3)=105

Lösung

16 x (x + 1) (x + 2) (x + 3) = 105

Lösung

x = \frac{1}{2}, x = - \frac{7}{2}, x = - \frac{3}{2} + i \frac{3}{2}, x = - \frac{3}{2} - i \frac{3}{2}

Schritte zur Lösung

16 x (x + 1) (x + 2) (x + 3) = 105

Schreibe

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

um:

16 x^{4} + 96 x^{3} + 176 x^{2} + 96 x

16 x^{4} + 96 x^{3} + 176 x^{2} + 96 x = 105

Verschiebe

105

auf die linke Seite

16 x^{4} + 96 x^{3} + 176 x^{2} + 96 x - 105 = 0

Faktorisiere

16 x^{4} + 96 x^{3} + 176 x^{2} + 96 x - 105 : (2 x - 1) (2 x + 7) (4 x^{2} + 12 x + 15)

(2 x - 1) (2 x + 7) (4 x^{2} + 12 x + 15) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

2 x - 1 = 0 or 2 x + 7 = 0 or 4 x^{2} + 12 x + 15 = 0

Löse

2 x - 1 = 0 : x = \frac{1}{2}

Löse

2 x + 7 = 0 : x = - \frac{7}{2}

Löse

4 x^{2} + 12 x + 15 = 0 : x = - \frac{3}{2} + i \frac{3}{2}, x = - \frac{3}{2} - i \frac{3}{2}

Die Lösungen sind

x = \frac{1}{2}, x = - \frac{7}{2}, x = - \frac{3}{2} + i \frac{3}{2}, x = - \frac{3}{2} - i \frac{3}{2}

Graph

Beliebte Beispiele

10 = 500 b^{3}

(x^2-9)^2-x^2+10=1

(x^{2} - 9)^{2} - x^{2} + 10 = 1

x^3-5x^2-2x+10=0

x^{3} - 5 x^{2} - 2 x + 10 = 0

8 x^{3} - 4 x = \frac{1}{2}

x^4+7x^3+6x^2-22x+8=0

x^{4} + 7 x^{3} + 6 x^{2} - 22 x + 8 = 0