The independent set polynomial is important in many areas of combinatorics, computer science, and statistical physics. For every integer Δ≥2, the Shearer threshold value λ⁎(Δ)=(Δ−1)Δ−1/ΔΔ. It known that for λ<−λ⁎(Δ), there are graphs G with maximum degree Δ whose polynomial, evaluated at λ, most 0. Also, no such any λ>−λ⁎(Δ). This paper motivated by computational problem approximating when λ<−λ...