of a type-I strongly regular graph.

The right-hand side of Equation  is a cubic polynomial in the indeterminate $t$ with positive leading coefficient. Furthermore, since for a type-I strongly regular graph we have $s = -(\sqrt{v}+1)/2$, we observe that the smallest zero of the right-hand side of Equation  is equal to $3/4 + ( \sqrt{v}-\sqrt{v+5/4} )/2$. Hence $C_\Gamma(r - t, 2 + 2r - 2t)$ is negative for $t < 3/4 + ( \sqrt{v}-\sqrt{v+5/4} )/2$. We use this observation in the next result, which can be used with Theorem \[thm:CliqueAdjPol\] to obtain the Delsarte bound for conference graphs.

\[cor:meetDelsarte\] Let $\Gamma$ be a type-I strongly regular graph with $v$ vertices. Then $$C_\Gamma \left ( \left \lfloor (\sqrt{v}-1)/2  \right \rfloor, \left \lfloor \sqrt{v} + 1 \right \rfloor \right ) < 0.$$

Let $t = {\operatorname{frac} \left ( r \right )}$. If $t > 1/2$ then $$C_\Gamma \left ( \left \lfloor (\sqrt{v}-1)/2  \right \rfloor, \left \lfloor \sqrt{v} + 1 \right \rfloor \right ) = C_\Gamma(r - t, 3 + 2r - 2t)$$ and the right-hand side of Equation  is negative for $t < 1$. Otherwise, if $t < 1/2$ then $$C_\Gamma \left ( \left \lfloor (\sqrt{v}-1)/2  \right \rfloor, \left \lfloor \sqrt{v} + 