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Beliebt Algebra >

x^4+x^3+10x^2+16x-96=0

Lösung

x^{4} + x^{3} + 10 x^{2} + 16 x - 96 = 0

Lösung

x = 2, x = - 3, x = 4 i, x = - 4 i

Schritte zur Lösung

x^{4} + x^{3} + 10 x^{2} + 16 x - 96 = 0

Faktorisiere

x^{4} + x^{3} + 10 x^{2} + 16 x - 96 : (x - 2) (x + 3) (x^{2} + 16)

(x - 2) (x + 3) (x^{2} + 16) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 2 = 0 or x + 3 = 0 or x^{2} + 16 = 0

Löse

x - 2 = 0 : x = 2

Löse

x + 3 = 0 : x = - 3

Löse

x^{2} + 16 = 0 : x = 4 i, x = - 4 i

Die Lösungen sind

x = 2, x = - 3, x = 4 i, x = - 4 i

Graph

Beliebte Beispiele

2 x^{5} - x + 1 = 0

(3x^2-13x+14)(x^2-4x+1)=0

(3 x^{2} - 13 x + 14) (x^{2} - 4 x + 1) = 0

solvefor y,x=(y+7)^3

so l v e f or y, x = (y + 7)^{3}

r^3+3r^2-9r-27=0

r^{3} + 3 r^{2} - 9 r - 27 = 0

v^{3} = 343