We determine sequences of polynomials with rational coefficients that have certain postulated values for their root power sums. These, in turn, determine four families of orthogonal polynomials that can be expressed in terms of Chebyshev polynomials by a change of variables. We examine properties of these sequences of polynomials, two of which have already been studied in a previous paper.
"Root power sums and Chebyshev polynomials." Rocky Mountain J. Math. 48 (1) 59 - 74, 2018. https://doi.org/10.1216/RMJ-2018-48-1-59