  Let $P(x)$ be a polynomial of degree $m$, with nonnegative and non-decreasing
coefficients. We settle the conjecture that for any positive real number $d$,
the coefficients of $P(x+d)$ form a unimodal sequence, of which the special
case $d$ being a positive integer has already been asserted in a previous work.
Further, we explore the location of modes of $P(x+d)$ and present some
sufficient conditions on $m$ and $d$ for which $P(x+d)$ has the unique mode
$\lceil{m-d\over d+1}\rceil$.
