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GCD of polynomials?

  1. Nov 21, 2008 #1

    tgt

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    Would the GCD of x^2+x+c and (x-a)^2+(x-a)+c always be 1?
     
  2. jcsd
  3. Nov 21, 2008 #2

    tiny-tim

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    Hi tgt! :smile:

    Hint: if the roots of the first one are p and q, what are the roots of the second one? :wink:
     
  4. Nov 21, 2008 #3

    tgt

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    So it seems that two polynomials have nonzero GCD when there is at leaste one root shared between the two. So any two polynomials of the form a(x-t)^2+b(x-t)+c and ax^2+bx+c must have GCD 1 since they wouldn't have any roots shared between them.
     
  5. Nov 22, 2008 #4

    tiny-tim

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    What about x2 + 3x + 2 = 0 and (x + 1)2 + 3(x + 1) + 2 = 0? :rolleyes:
     
  6. Nov 22, 2008 #5

    tgt

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    ok, I wasn't thinkng clearly at the time.
     
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