  We classify rooted trees which have strictly unimodal q-polynomials (plucking
polynomial). We also give criteria for a trapezoidal shape of a plucking
polynomial. We generalize results of Pak and Panova on strict unimodality of
q-binomial coefficients. We discuss which polynomials can be realized as
plucking polynomials and whether or not different rooted trees can have the
same plucking polynomial.
