On the Zeros of Quaternionic Polynomials with Restricted Coefficient

Let P(z)=∑ⱼ₌₀ⁿaⱼzʲ be a polynomial of degree n such that aₙ≥ aₙ₋₁≥...≥ a₁≥ a₀≥ 0 . Then according to Eneström–Kakeya theorem all the zeros of $$P(z)$$ lie in |z|≤ 1 . This important result was recently extended to quaternionic setting by Carney, Gardner, Keaton, and Powers. In this paper, we shall generalize and refine the results of Carney, Gardner, Keaton, Powers, and Tripathi.