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The roots (sometimes also called "zeros") of an equation f(x)=0 are the values of x for which the equation is satisfied. Roots x which belong to certain sets are usually ...

A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments. In general, a theorem is an embodiment of some general ...

For an arbitrary not identically constant polynomial, the zeros of its derivatives lie in the smallest convex polygon containing the zeros of the original polynomial.

The zeros of the derivative P^'(z) of a polynomial P(z) that are not multiple zeros of P(z) are the positions of equilibrium in the field of force due to unit particles ...

If any of the roots of a polynomial are increased, then all of the critical points increase.

Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

A multiple root is a root with multiplicity n>=2, also called a multiple point or repeated root. For example, in the equation (x-1)^2=0, 1 is multiple (double) root. If a ...

A root having multiplicity n=1 is called a simple root. For example, f(z)=(z-1)(z-2) has a simple root at z_0=1, but g=(z-1)^2 has a root of multiplicity 2 at z_0=1, which is ...

The operation of taking an nth root of a number.

A graph G whose line graph is L(G) is called the root graph R(L(G)) of L(G). In order words, R(L(G))=G. The root graph of a connected graph is unique except for K_3=C_3 (the ...