mikkimcutchen mikkimcutchen
  • 11-07-2022
  • Mathematics
contestada

what are the zeros of the function f(x)=x^4-4x^2-5

Respuesta :

LiliactheSilkwing
LiliactheSilkwing LiliactheSilkwing
  • 11-07-2022

Answer:

[tex]x =\sqrt{5} ,-\sqrt{5} ,-i,i[/tex]

Step-by-step solution:

[tex]0=x^4-4x^2-5[/tex]   [tex]u = x^2[/tex]
[tex]0 = u^2-4u-5[/tex]
[tex]0 = (u -5)(u+1)[/tex]
[tex]u = 5[/tex]  [tex]u=-1[/tex]
[tex]x^2 =5[/tex]    [tex]x^2 = -1[/tex]
[tex]x= +-\sqrt{5}[/tex]   [tex]x = +-i[/tex]

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