It depends on what you can use (any methods of calculus?) and the level of strictness. Basically, if you look at the graph of
, this is obvious, but the question is, how much handwaving you are allowed to use in referring to the graph.
The function
behaves like
in that it is positive on
and negative on
for
and it is zero in
,
. However, the amplitude increases exponentially. You can see the graph in WolframAlpha. So if
are three positive roots of
, then there is an interval
either inside
or inside
(or both, if these are not consecutive roots), where
is negative. Also, one can show that even in the first negative dip between
and
, the function's minimum is far less than -1/2.