Abstract Let p(z) be a complex polynomial of degree n, having k of its zeros in the unit disc. We prove that at least one zero of p(k−1)(z) lies in the disc |z| ≤ 2(n−k+1) ln 2 . application/pdf 393221 bytes Comptes rendus de l’Académie bulgare des Sciences volume: 78 number: 5 startpage: 651 endpage: 655 eng Bulgarian Academy of Sciences 2025 https://phaidrabg.bg.ac.rs/o:37487 doi:10.7546/CRABS.2025.05.01 ISSN: 1310–1331 info:eu-repo/semantics/article On the Problem of Kakeya Key words: zeros of polynomial, critical points of a polynomial, apolar polynomials 2020 Mathematics Subject Classification: Primary 26C10, Seconda- ry 30C15 All rights reserved Bakić, Radoš