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Beliebt Algebra >

p^3+2p+3=0

Lösung

p^{3} + 2 p + 3 = 0

Lösung

p = - 1, p = \frac{1}{2} + i \frac{11}{2}, p = \frac{1}{2} - i \frac{11}{2}

Schritte zur Lösung

p^{3} + 2 p + 3 = 0

Faktorisiere

p^{3} + 2 p + 3 : (p + 1) (p^{2} - p + 3)

(p + 1) (p^{2} - p + 3) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

p + 1 = 0 or p^{2} - p + 3 = 0

Löse

p + 1 = 0 : p = - 1

Löse

p^{2} - p + 3 = 0 : p = \frac{1}{2} + i \frac{11}{2}, p = \frac{1}{2} - i \frac{11}{2}

Die Lösungen sind

p = - 1, p = \frac{1}{2} + i \frac{11}{2}, p = \frac{1}{2} - i \frac{11}{2}

Graph

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