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Repeated roots

  1. Nov 10, 2005 #1
    If ar^2+br+c=0 has equal roots r1, show that
    L[e^(rt)]=a(e^(rt))``+b(e^(rt))`+ ce^(rt)=a{(r-r1)^2}e^(rt)

    could someone offer some advice?
  2. jcsd
  3. Nov 10, 2005 #2


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    Staff Emeritus
    Science Advisor

    The only advice I can give is that you go ahead and do what is shown on the left hand side!
    Surely, you know what the first and second derivatives of ert are!
    And, of course, If r1 is a double root of ar2+ br+ c= 0, then ar2+ br+ c= a(r- r1[/sup])(r-r2).
    Last edited: Nov 12, 2005
  4. Nov 11, 2005 #3
    ok ~ thanks!
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