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We investigate the interlacing of zeros of polynomials of different degreeswithin the sequences of $q$-Laguerre polynomials$\left\{\tilde{L}_n^{(\delta)}(z;q)\right\}_{n=0}^{\infty}$ characterized by$\delta\in(-2,-1).$ The interlacing of zeros of quasi-orthogonal polynomials$\tilde{L}_n^{(\delta)}(z;q)$ with those of the orthogonal polynomials$\tilde{L}_m^{(\delta+t)}(z;q), m,n\in\mathbb{N}, t\in\{1,2\}$ is alsoconsidered. New bounds for the least zero of the (order $1$) quasi-orthogonal$q$-Laguerre polynomials are derived.

Zeros of quasi-orthogonal $q$-Laguerre polynomials