\documentclass[a4paper]{article}
\usepackage{tkz-tab}
\usepackage{xpatch}

% tkz-tab hardcodes $0$ for the zeros
\xpatchcmd{\tkzTabLine}{$0$}{$\bullet$}{}{}
% we want solid lines
\tikzset{t style/.style={style=solid}}

\begin{document}

\begin{tikzpicture}
\tkzTabInit[lgt=2,espcl=2,deltacl=0]
  { /.8, $2(1-x^{2})$ /.8, $(1+x^{2})^{2}$ /.8, $f'(x)$ /.8, $4x$ /.8, $(x^{2}-3)$ /.8, $(1+x^{2})^{3}$ /.8, $f''(x)$ /.8,}
  {,$-\sqrt{3}$,$-1$,$0$, $1$, $\sqrt{3}$, } % four main references
\tkzTabLine {,-,t,-,z,+,t,+,z,-,t,-,} % seven denotations
\tkzTabLine {,+,t,+,t,+,t,+,t,+,t,+,}
\tkzTabLine {,-,t,-,z,+,t,+,z,-,t,-,}
\tkzTabLine {,-,t,-,t,-,z,+,t,+,t,+,}
\tkzTabLine {,+,z,-,t,-,t,-,t,-,z,+,}
\tkzTabLine {,+,t,+,t,+,t,+,t,+,t,+,}
\tkzTabLine {,-,z,+,t,+,z,-,t,-,z,+,}
\end{tikzpicture}

\end{document}