  We consider interlacing properties satisfied by the zeros of Jacobi
polynomials in quasi-orthogonal sequences characterised by $\alpha>-1$,
$-2<\beta<-1$. We give necessary and sufficient conditions under which a
conjecture by Askey, that the zeros of Jacobi polynomials $P_n^{(\alpha,
\beta)}$ and $P_{n}^{(\alpha,\beta+2)}$ are interlacing, holds when the
parameters $\alpha$ and $\beta$ are in the range $\alpha>-1$ and $-2<\beta<-1$.
We prove that the zeros of $P_n^{(\alpha, \beta)}$ and
$P_{n+1}^{(\alpha,\beta)}$ do not interlace for any $n\in\mathbb{N}$, $n\geq2$
and any fixed $\alpha$, $\beta$ with $\alpha>-1$, $-2<\beta<-1$. The
interlacing of zeros of $P_n^{(\alpha,\beta)}$ and $P_m^{(\alpha,\beta+t)}$ for
$m,n\in\mathbb{N}$ is discussed for $\alpha$ and $\beta$ in this range, $t\geq
1$, and new upper and lower bounds are derived for the zero of
$P_n^{(\alpha,\beta)}$ that is less than $-1$.
