A ring $R$ with a monomorphism $\alpha$ and an $\alpha$-derivation
$\delta$ with $\alpha\delta=\delta\alpha$ is called
(\textit{$\alpha$,$\delta$})-\textit{quasi Baer} (resp.
\textit{quasi Baer}) if the right annihilator of every
($\alpha$,$\delta$)-ideal (resp. ideal) of $R$ is generated by an
idempotent of $R$. In this paper we show that  a semiprime ring
\textit{$R[x;\alpha,\delta] $} is $\alpha$-quasi Baer if and only
if $S=R[x;\alpha ,\delta ]$ is $(\alpha,\overline{\delta })$-quasi
Baer for every extended $\alpha $-derivation $\overline{\delta}$
on $S$ of $\delta$ if and only if $R$ is
($\alpha,\delta $)-quasi Baer. \\