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Homework Help: Finding Zeros of a function

  1. Jan 18, 2005 #1
    hey.. how would i find the zeros of the following function:

    f(x)=x^4-25

    I tried inputting the value into my caculator and then go to table find y values that equal 0 in x and i only found -25.. how do i find the rest?


    thanks
     
  2. jcsd
  3. Jan 18, 2005 #2

    jamesrc

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    -25 shouldn't be one of the zeros. You can find the two real zeros graphically, but why not do it algebraically?

    x4 - 25 = 0
    x4 = 25
    x2 = {-5, +5}
    and so on...
     
  4. Jan 18, 2005 #3
    [tex]x^4-25=0[/tex]
    [tex]x^4=25[/tex]
    [tex]x^2=5[/tex]
    [tex]x=+-/sqrt{5}[/tex]
     
    Last edited: Jan 18, 2005
  5. Jan 18, 2005 #4
    hey vitaly, do you by any chance live in Ohio? just guessing....
     
  6. Jan 18, 2005 #5
    Nope... What makes you say that?
     
  7. Jan 18, 2005 #6
    i knew a person by the name Vitaly there, but i guess it is a common name.. so i was being unrealistic....
     
  8. Jan 18, 2005 #7
    Oh, well I live in TN....

    Is the person you knew Russian? I have never met anybody else with my name before. Most people think it's weird; it's definitely not common here.
     
  9. Jan 18, 2005 #8
    yup, they were russians.. infact there was two of them cause they were twins...
     
  10. Jan 18, 2005 #9
    ok that was a stupid question... didnt think of that for some odd reason.. thanks much for ur help1
     
  11. Jan 18, 2005 #10

    Hurkyl

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    For the sake of precision, from:

    x^4 = 25

    you should deduce

    x^2 = 5 or x^2 = -5

    and not just the first one.


    Actually, I'm a big fan of using factoring instead of these types of manipulations. e.g.

    x^4 = 25
    x^4 - 25 = 0
    (x^2 - 5)(x^2 + 5) = 0
     
  12. Jan 18, 2005 #11

    dextercioby

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    To continue from where Hurkyl left off:

    [tex] x^{4}-25=(x-\sqrt{5})(x+\sqrt{5})(x-i\sqrt{5})(x+i\sqrt{5})=0 [/tex]

    I think the solutions are obvious.

    Daniel.
     
  13. Jan 23, 2005 #12
    Obvious? Probably not to jai6638
     
  14. Jan 23, 2005 #13

    dextercioby

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    And how did u know that??Did u talk to him?? :wink:

    Daniel.
     
  15. Jan 23, 2005 #14
    i got it.... thanks much! :)
     
  16. Jan 25, 2005 #15
    Well, he(she?) didn't know how to find the zeros of x^4-25. From that I can infer that you statement might not be very obvious to him(her?).
     
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