How to make the same font size for both numerator and denominator?

It looks like a bug in pst-eucl. As a workaround, you can use \dfrac instead (load amsmath), and slightly increase the value of PointNameSep:

\documentclass[pstricks, border=0pt,12pt]{standalone}
\usepackage{pst-eucl}
\usepackage{amsmath, nccmath}
\usepackage{etoolbox}
\robustify\sqrt

\begin{document}

\begin{pspicture}(-6,-1.25)(6,1.25)
    \pstGeonode[
        PointSymbol=|,
        PosAngle=-90,
        PointNameSep=18 pt,
        PointName={\dfrac{3-\sqrt{17}}{2},-\dfrac{1}{2},\dfrac{3}{2},2, \dfrac{3+\sqrt{17}}{2}}
    ](-4,0){A}(-2,0){B}(0,0){C}(2,0){D}(4,0){E}
    \pcline[nodesep=-1](A)(E)
    \pcline(5.8,0)(E)\nbput{$++++$}
    \pcline(E)(D)\nbput{$----$}
    \pcline(D)(C)\nbput{$++++$}
    \pcline(C)(B)\nbput{$----$}
    \pcline(B)(A)\nbput{$++++$}
    \pcline(A)(-5.8,0)\nbput{$----$}
    \psset{arrows=*-*,offset=22pt}
    \pcline(A)(B)
    \pcline(C)(D)
    \pcline{*->}(E)(5.5,0)
\end{pspicture}

\end{document} 

For reasons that depend on the same ones that force to \robustify\sqrt, a fraction as the first item is typeset incorrectly. You can \robustify also \frac.

\documentclass[pstricks,border=0pt,12pt]{standalone}
\usepackage{pst-eucl}
\usepackage{etoolbox,amsmath}
\robustify\sqrt
\robustify\frac

\begin{document}
\begin{pspicture}(-6,-1)(6,1.25)
    \pstGeonode[
        PointSymbol=|,
        PosAngle=-90,
        PointNameSep=16pt,
        PointName={\frac{3-\sqrt{17}}{2},-\frac{1}{2},\frac{3}{2},2,\frac{3+\sqrt{17}}{2}}
    ](-4,0){A}(-2,0){B}(0,0){C}(2,0){D}(4,0){E}
    \pcline[nodesep=-1](A)(E)
    \pcline(5.8,0)(E)\nbput{${+}{+}{+}{+}$}
    \pcline(E)(D)\nbput{${-}{-}{-}{-}$}
    \pcline(D)(C)\nbput{${+}{+}{+}{+}$}
    \pcline(C)(B)\nbput{${-}{-}{-}{-}$}
    \pcline(B)(A)\nbput{${+}{+}{+}{+}$}
    \pcline(A)(-5.8,0)\nbput{${-}{-}{-}{-}$}
    \psset{arrows=*-*,offset=22pt}
    \pcline(A)(B)
    \pcline(C)(D)
    \pcline{*->}(E)(5.5,0)
\end{pspicture}
\end{document}

Also bracing each item works, but using a robust \frac is better.

Note: due to + and - being binary operation symbols, a sequence such as ++++ is interpreted as Ord Bin Ord Ord (by rule a binary operation symbol is changed into an ordinary one if it doesn't have suitable operands on either side) and the spacing is odd. Input them as {+}{+}{+}{+} and {-}{-}{-}{-} to get all ordinary symbols.

It is completely nonsense to use the PointName key for such labels because the label is internally also the node name. You should use simple nodes and \psxTick instead. However,

PointName={{\frac{3-\sqrt{17}}{2}},{-\frac{1}{2}},{\frac{3}{2}},{\scriptstyle2},{\frac{3+\sqrt{17}}{2}}}

should also do the trick

\documentclass[pstricks,border=0pt,12pt]{standalone}
\usepackage{pstricks-add}

\begin{document}
\begin{pspicture}(-6,-1)(6,1.25)
    \pnodes(-4,0){A}(-2,0){B}(0,0){C}(2,0){D}(4,0){E}
    \psxTick(-4){\frac{3-\sqrt{17}}{2}}
    \psxTick(-2){-\frac{1}{2}}
    \psxTick(0){\frac{3}{2}}
    \psxTick(2){\scriptstyle2\vphantom{\frac12}}
    \psxTick(4){\frac{3+\sqrt{17}}{2}}
    \multido{\rA=-4.9+4.0}{3}{\uput[90](\rA,0){$----$}}%
    \multido{\rA=-3+4}{3}{\uput[90](\rA,0){$++++$}}%
    \pcline[nodesep=-1.75](A)(E)
    \psset{arrows=*-*,offset=22pt}
    \pcline(A)(B)
    \pcline(C)(D)
    \pcline{*->}(E)(5.5,0)
\end{pspicture}
\end{document}

Or if you do not like hardcoded values:

\documentclass[pstricks,border=0pt,12pt]{standalone}
\usepackage{pstricks-add}
\begin{document}
\begin{pspicture}(-6,-1)(6,1.25)
    \pnodes(-4,0){A}(-2,0){B}(0,0){C}(2,0){D}(4,0){E}
    \psxTick(-4){\frac{3-\sqrt{17}}{2}}
    \psxTick(-2){-\frac{1}{2}}
    \psxTick(0){\frac{3}{2}}
    \psxTick(2){\scriptstyle2\vphantom{\frac12}}
    \psxTick(4){\frac{3+\sqrt{17}}{2}}
    \pcline[nodesep=-1.75](A)(E)
    \psset{arrows=*-*,offset=20pt}
    \pcline(A)(B)\nbput{$++++$}
    \pcline(C)(D)\nbput{$++++$}
    \pcline{*->}(E)(5.5,0)\nbput{$++++$}
    \psset{linestyle=none,arrows=-}
    \pcline(-5.8,0)(A)\nbput{$----$}
    \pcline(B)(C)\nbput{$----$}
    \pcline(D)(E)\nbput{$----$}
\end{pspicture}
\end{document}