Question

explain in brief about polynomials and their zeroes​

Answer 1

Answer:

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function {\displaystyle f} f is a member {\displaystyle x} x of the domain of {\displaystyle f} f such that {\displaystyle f(x)} f(x) vanishes at {\displaystyle x} x; that is, {\displaystyle x} x is a solution of the equation {\displaystyle f(x)=0} f(x)=0. In other words, a "zero" of a function is an input value that produces an output of {\displaystyle 0} {\displaystyle 0}.[1]

A root of a polynomial is a zero of the corresponding polynomial function. The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree and that the number of roots and the degree are equal when one considers the complex roots (or more generally the roots in an algebraically closed extension) counted with their multiplicities. For example, the polynomial {\displaystyle f} f of degree two, defined by