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Beliebt Algebra >

8x^3+18x^2+45x+27=0

Lösung

8 x^{3} + 18 x^{2} + 45 x + 27 = 0

Lösung

x = - \frac{3}{4}, x = - \frac{3}{4} + i \frac{3 7}{4}, x = - \frac{3}{4} - i \frac{3 7}{4}

Schritte zur Lösung

8 x^{3} + 18 x^{2} + 45 x + 27 = 0

Faktorisiere

8 x^{3} + 18 x^{2} + 45 x + 27 : (4 x + 3) (2 x^{2} + 3 x + 9)

(4 x + 3) (2 x^{2} + 3 x + 9) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

4 x + 3 = 0 or 2 x^{2} + 3 x + 9 = 0

Löse

4 x + 3 = 0 : x = - \frac{3}{4}

Löse

2 x^{2} + 3 x + 9 = 0 : x = - \frac{3}{4} + i \frac{3 7}{4}, x = - \frac{3}{4} - i \frac{3 7}{4}

Die Lösungen sind

x = - \frac{3}{4}, x = - \frac{3}{4} + i \frac{3 7}{4}, x = - \frac{3}{4} - i \frac{3 7}{4}

Graph

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