The nature and co-ordinates of roots can be determined using the discriminant and solving polynomials as part of Bitesize Higher Maths ...

In the 1800s, prior to Hilbert’s list of problems, mathematicians discovered that the roots of unity could serve as “building blocks” for the particular collection of numbers that they wanted to study ...

Lior Bary-Soroker, Ofir Gorodetsky, Roots of Polynomials and the Derangement Problem, The American Mathematical Monthly, Vol. 125, No. 10 (DECEMBER 2018), pp. 934-938 ...

This paper concerns the location of roots of polynomials with respect to the principal coordinate axes (referred to generally as the Routh-Hurwitz criteria and the Sturm criteria). It provides a new ...