In his beautiful monograph, Mark Kac gave a proof of Vieta's formula using the Rademacher functions and their independence property. In the first chapter of his book, he gave as an exercise to state and prove a generalization of Vieta's formula. In this paper we give a proof based on Kac's proof for Vieta's formula, and to the best of our knowledge, this generalization has only been achieved by Kent E. Morrison using the Fourier transform and delta distributions.
Mohamed Ben Rhouma
"Generalization of Vieta's Formula,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 7:
1, Article 14.
Available at: https://scholar.rose-hulman.edu/rhumj/vol7/iss1/14