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Beliebt Algebra >

x^4-x^3-7x^2-14x-24=0

Lösung

x^{4} - x^{3} - 7 x^{2} - 14 x - 24 = 0

Lösung

x = - 2, x = 4, x = - \frac{1}{2} + i \frac{11}{2}, x = - \frac{1}{2} - i \frac{11}{2}

Schritte zur Lösung

x^{4} - x^{3} - 7 x^{2} - 14 x - 24 = 0

Faktorisiere

x^{4} - x^{3} - 7 x^{2} - 14 x - 24 : (x + 2) (x - 4) (x^{2} + x + 3)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x + 2 = 0 : x = - 2

Löse

x - 4 = 0 : x = 4

Löse

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

Die Lösungen sind

x = - 2, x = 4, x = - \frac{1}{2} + i \frac{11}{2}, x = - \frac{1}{2} - i \frac{11}{2}

Graph

Beliebte Beispiele

x^4-4x^3+2x^2-x+1=0

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

x^{3} - 19 = 8

x^{2} + 5 = x^{5} - 2

a^8-a^7=5,a^1=3

a^{8} - a^{7} = 5, a^{1} = 3

(x - 7)^{4} = 62 5^{7}