let
be the double root. then
i.e.
which we'll call it (1), and
which we'll call it (2). if
then (1) and (2) gives us b = c = 0, and what you want
to prove obviously holds. so i'll assume that
multiply (1) by 3 and (2) by
and then add the result
together to get
call this (3). now multiply (2) by
and (3) by
and then add the result
together to get
call this one (4). now multiply (2) by
and (3) by
and then
add the result together to get
call this (5). finally multiply (4) by
and (5)
by
and add the result together to get