# Repeated roots

1. Nov 10, 2005

### asdf1

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)

2. Nov 10, 2005

### HallsofIvy

Staff Emeritus
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
3. Nov 11, 2005

ok ~ thanks!