Polynomial Pell's equation

Consider the polynomial Pell's equation $X^2 -DY^2 = 1$, where $D = A^2 + 2C$is a monic polynomial in ${\mathcal Z}[x]$ and $\deg{C} < \deg{A}$. Then for $A, C \in {\mathcal Q}[x]$, $\deg{C} < 2$, and $B = A/C \in {\mathcal Q}[x]$, a necessary and sufficient condition for the polynomial Pell's equation to have a nontrivial solution in ${\mathcal Z}[x]$ is obtained.