A symbol for a checkmark to indicate something is correct:

\newcommand{\correct}{$\color{green}\tikz\fill[scale=0.4](0,.35) -- (.25,0) -- (1,.7) -- (.25,.15) -- cycle;$}

A symbol for a cross to indicate something is wrong:

\newcommand{\wrong}{$\mathbin{\tikz [x=1.4ex,y=1.4ex,line width=.2ex, red] \draw (0,0) -- (1,1) (0,1) -- (1,0);}$}%

You’ll need TikZ for this.