👉 Learn how to write the equation of a polynomial when given complex zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the ...

👉 Learn about Descartes' Rule of Signs. Descartes' rule of signs is used to determine the number of positive and negative real zeros of a polynomial function. Knowing the number of positive and ...

Harmonic polynomials, constructed as sums of analytic and conjugate-analytic components, present a rich interplay between complex analysis and geometric function theory. Unlike purely analytic ...

Permutation polynomials over finite fields form a central theme in modern algebraic research, intertwining group theory, number theory and combinatorial design. A finite field is a set of elements ...

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them. Problems in ...