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Please help me with this

  1. Apr 10, 2005 #1
    please help me with this!!

    f(x)=3x^2+7x=5. find the solution of f(x)==0(mod m) for


    the only thing i have done so far is completed the square
  2. jcsd
  3. Apr 11, 2005 #2
    Completing the square gives (X+7/6)^2=109/36.

    Bringing the 36 to the other side gives: (6X+7)^2 =109.

    For modulo 23, you should consider quadratic reciprocity. For M=25, the problem is easier.
    Last edited: Apr 11, 2005
  4. Apr 12, 2005 #3


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    I'll assume you mean [tex]f(x)=3x^2+7x-5[/tex] (that is, you're not setting it to a boolean value).

    I'm not convinced that completing the square is relevant here. A quick use of quadratic reciprocity (don't worry, skip it if you haven't seen it) shows that there are no solutions modulo 23:



    This doesn't mean anything, though, just that the real solution isn't on one of the modular solutions.

    Look at it this way: replacing [tex]x[/tex] with [tex]x+1[/tex] you have [tex]f(x)=3x^2+6x+1+7x+1-5=(3x^2+7x-5)+(6x+2)[/tex]. By choosing [tex]x[/tex] you should be able to cycle through all the congruence classes, since neither 23 nor 25 is divisible by 2 or 6.
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