Counting Interior Roots of Trinomials

On the number of roots for harmonic trinomials

“…Despite the apparent simplicity of (1.1), the well-known works of P. Ruffini, N.H. Abel and É. Galois imply that for n + m ≥ 5 and generic trinomials of the form (1.1) there is no formula for their roots in terms of the so-called radicals. For the literature reporting geometric, topological, quantitative and qualitative behavior of the roots for trinomials of the form (1.1) we refer to [2,3,4,5,7,8,9,10,14,15,16,17,18,20,21,28,33,35,43,44,45,52,53] and the references therein. The professor Jenő Egérvary was a prominent Hungarian mathematician who did important contributions in several areas of mathematics such as: algebraic equations, analysis, combinatorics, differential equations, function theory, geometry, matrix theory and its applications, optimization, theoretical physics, theory of determinants.…”