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Homework Help: Find the zeros of the function algebraically

  1. Jan 21, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the zeros of the function algebraically


    2. Relevant equations
    f(x)=x/(9x^2-4)
    and
    f(x)=x^3-x

    3. The attempt at a solution
    i was gone for about a month and a half from the class because i had to move and im kinda rusty
    ATTEMPT-

    f(x)=x/(9x^2-4)
    Multiplied by x
    subtracted 9x^2
    and added 4, which gave me.....
    -9x^2+x+4=f(x) then i put it in a quadratic formula to find it and i got the wrong answer (i checked in the back of the book for the answer which was 0, i know im probly really wrong but i was away from the class a long time lol.

    Second problem
    f(x)=x^3-x
    I honestly completely forgot how to solve for the zeros of a cubic function sorry :(
     
  2. jcsd
  3. Jan 21, 2010 #2

    Mark44

    Staff: Mentor

    For the first one, the only time a rational expression (e.g., x/(9x^2 - 4)) can be zero is when the numerator is zero.

    This doesn't make any sense.
     
  4. Jan 21, 2010 #3

    Mark44

    Staff: Mentor

    For the 2nd problem, factor x^3 - x.

    Frankly, missing a month and a half of a math class, regardless of whether the reason is good or not, might be insurmountable.
     
  5. Jan 21, 2010 #4
    oops i put in the problem wrong and i figured it out(the second one)
    f(x)=1/2x^3-x
    x(1/2x^2-1)=0
    x=0
    1/2x^2-1=0
    1/2x^2=1
    x^2=2
    x= +-square root of 2

    Thank you for your assistance.
     
  6. Jan 21, 2010 #5

    Char. Limit

    User Avatar
    Gold Member

    Watch out on that second equation... you forgot about the x you factored out.

    A cubic equation has three zeros.
     
  7. Jan 22, 2010 #6

    Mentallic

    User Avatar
    Homework Helper

    No he didn't! :smile:



    it would suck if the OP were a girl. Still, I prefer assuming than typing in he/she.
    They should really create a word to indicate either sex!
     
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