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Bi-variate Non-Homogeneous Polynomial Conceptual Question

  1. Sep 25, 2013 #1
    1. The problem statement, all variables and given/known data
    I have found the roots of my polynomial:
    ## (2x+3y)^{2}-1 =0 ##
    Roots are x=3n+2 & y=-2n-1, where n belongs to all Z.
    What does it mean that the solution has arbitrary large coordinates?

    3. The attempt at a solution
    I think I know the basic concept of root. It could be that in this case the surface (has defined solutions) intersect some other plane at 0 in both points
    Also, if it has arbitrary large coordinates as roots, it is because the axis of the surface or part of the surface runs through all solutions in the form above.
    Am I right?

    Thank you.
     
  2. jcsd
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