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{\bf Shi-Mei Ma and Yi Wang}
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{\bf $q$-Eulerian Polynomials and Polynomials with Only Real Zeros}
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Let $f$ and $F$ be two polynomials satisfying
$F(x)=u(x)f(x)+v(x)f'(x)$. We characterize the relation between the
location and multiplicity of the real zeros of $f$ and $F$, which
generalizes and unifies many known results, including the results of
Brenti and Br\"and\'en about the $q$-Eulerian polynomials.



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