  Let $G = (V, E)$ be a simple graph of order $n$. The total dominating set of
$G$ is a subset $D$ of $V$ that every vertex of $V$ is adjacent to some
vertices of $D$. The total domination number of $G$ is equal to minimum
cardinality of total dominating set in $G$ and is denoted by $\gamma_t(G)$. The
total domination polynomial of $G$ is the polynomial
$D_t(G,x)=\sum_{i=\gamma_t(G)}^n d_t(G,i)x^i$, where $d_t(G,i)$ is the number
of total dominating sets of $G$ of size $i$. A root of $D_t(G, x)$ is called a
total domination root of $G$. The set of total domination roots of graph $G$ is
denoted by $Z(D_t(G,x))$. In this paper we show that $D_t(G,x)$ has $\delta-2$
non-real roots and if all roots of $D_t(G,x)$ are real then $\delta\leq 2$,
where $\delta$ is the minimum degree of vertices of $G$. Also we show that if
$\delta\geq 3$ and $D_t(G,x)$ has exactly three distinct roots, then
$Z(D_t(G,x))\subseteq \{0, -2\pm \sqrt{2}i, \frac{-3\pm \sqrt{3}i}{2}\}$.
Finally we study the location roots of total domination polynomial of some
families of graphs.
