Question

Is the order of growth of any polynomial with complex coefficients zero? why?

Is the order of growth of any polynomial with complex coefficients zero? why?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
what is the order of growth of any polynomial?
what is the order of growth of any polynomial?
If p(x) is a complex polynomial with real coefficients, it is well known that it can...
If p(x) is a complex polynomial with real coefficients, it is well known that it can be factored into a product of linear and quadratic terms with real coefficients, or into a product of linear terms only if the coefficients are allowed to be complex. First, use Maple to write q(z) = x5 −3x4 −3x3 +9x2 −10x+30 as a product of exact linear and quadratic factors with real coefficients. By exact, I mean you should leave any non-rational factors expressed...
Given a zero of the polynomial, determine all other zeros (real and complex) and write the...
Given a zero of the polynomial, determine all other zeros (real and complex) and write the polynomial in terms of a product of linear factors: x4-5x2+10x-6
1. Find a polynomial equation with real coefficients that has given zeros. 3 - 7i and...
1. Find a polynomial equation with real coefficients that has given zeros. 3 - 7i and 3 + 7i The equation is x2 - ___x + ___ = 0 2. Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. f(x) = x4 +10x3 - 31x2 + 80x - 312 All complex zeros are ____ 3. Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. f(x) =...
Find an equation for f(x), the polynomial of smallest degree with real coefficients such that f(x)...
Find an equation for f(x), the polynomial of smallest degree with real coefficients such that f(x) bounces off of the x-axis at 5, breaks through the x-axis at −1, has complex roots of −5−3i and −4+2i and passes through the point (0,89).
Find an equation for f(x), the polynomial of smallest degree with real coefficients such that f(x)...
Find an equation for f(x), the polynomial of smallest degree with real coefficients such that f(x) breaks through the x-axis at −5, breaks through the x-axis at −4, has complex roots of 5−i and −3−5i and passes through the point (0,68).
Let f(x) be a cubic polynomial of the form x^3 +ax^2 +bx+c with real coefficients. 1....
Let f(x) be a cubic polynomial of the form x^3 +ax^2 +bx+c with real coefficients. 1. Deduce that either f(x) factors in R[x] as the product of three degree-one polynomials, or f(x) factors in R[x] as the product of a degree-one polynomial and an irreducible degree-two polynomial. 2.Deduce that either f(x) has three real roots (counting multiplicities) or f(x) has one real root and two non-real (complex) roots that are complex conjugates of each other.
(a) For a polynomial x2 + bx + c, give the coefficients in terms of its...
(a) For a polynomial x2 + bx + c, give the coefficients in terms of its roots: α1 and α2. (b) For a monic, cubic polynomial, give the coefficients in terms of its roots. (c) Generalize these result to monic polynomials of higher degree
Let R be the polynomial ring in infinitly many variables x_1,x_2,.... with coefficients in a field...
Let R be the polynomial ring in infinitly many variables x_1,x_2,.... with coefficients in a field F. Let M be the cyclic R- module R itself. Prove that the submodule {x_1,x_2,....} cannot be generated by any finite set.
a)Give an example of a polynomial with integer coefficients of degree at least 3 that has...
a)Give an example of a polynomial with integer coefficients of degree at least 3 that has at least 3 terms that satisfies the hypotheses of Eisenstein's Criterion, and is therefore irreducible. b)Give an example of a polynomial with degree 3 that has at least 3 terms that does not satisfy the hypotheses of Eisenstein's Criterion.