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Find an annihilator of x^2 + 2x^5

  1. Aug 17, 2016 #1
    1. The problem statement, all variables and given/known data
    Find an annihilator of x2+2x5.

    2. Relevant equations
    xnecx -----> [D-c]n+1

    [Q1(D)Q2(D)] = b1(x) + b2(x)
    3. The attempt at a solution

    x2 -----> D3

    2x5-----> D6

    x2 + 2x5 ------> (D3)(D6) = D18

    The answer should be D6.
     
    Last edited by a moderator: Aug 17, 2016
  2. jcsd
  3. Aug 17, 2016 #2

    Mark44

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    Doesn't the D6 operator also annihilate x2?
     
  4. Aug 17, 2016 #3
    I guess it does. So does that mean there can be multiple annihilators and they'll all work? Or should you always pick the least common multiple?
     
  5. Aug 17, 2016 #4

    vela

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    What does the last line mean? It's not clear to me.

    Why are you multiplying the two annihilators?
     
  6. Aug 17, 2016 #5

    Mark44

    Staff: Mentor

    Didn't notice this before -- is x3x6 = x18?
     
  7. Aug 17, 2016 #6

    Mark44

    Staff: Mentor

    Dn+1 annihilates xn and all lower powers of x. I don't see that this is related to the LCM in any way.
     
  8. Aug 17, 2016 #7

    vela

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    Heh...I didn't notice that either.
     
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