Determine stability of a system using the Routh-Hurwitz stability criterion
Haskell - 264 bytes

p(a:b:s)=(a,b):p s
p[a]=[(a,0)]
p[]=[]
s((a:w),m@(b:v))=a:s(m,m%zipWith(\c d-&gt;(b*c-a*d)/b)w v)
s((a:_),_)=[a]
m%(0:v)|all(==0)v=fst$foldr(\b(d,p)-&gt;(b*p:d,2+p))([],0)m
m%v=v
q(a:s)|all((&gt;0).(a*))s="1\n"
q _="0\n"
main=interact$(&gt;&gt;=q.s.unzip.p.map read.words).lines


Running the sample inputs:

&amp; runhaskell 11847-Stability.hs 
1 12 6 10 10 6 14
1 1 -2
1 2 1 2
1 3 1 3 16
1 2 3 6 2 1
1 2 14 88 200 800
1 2 3 6 2 1
1 3 6 12 8
1 4 5 2 4 16 20 8
0
0
1
0
0
0
0
1
0


(The output is interleaved with the input if you type it one line at a time, as per spec. If you bulk paste, you see all the output after the input.)