Zeros of a Polynomial

Given a polynomial function of degree there are some obvious questions that can be difficult to answer.

    (i) How many zeros of are real and how many are complex?
    
    (ii) How many zeros are positive and how many are negative?
    
    (iii) Ho many zeros are rational and how many are irrational?
    
The following famous theorem is called The Fundamental  of Algebra and give is a good starting point for these questions.

Theorem (Zeros of a Polynomial) Fundamental Theorem of Algebra. If a polynomial has positive degree and complex coefficients, then has at least one complex zero.

Theorem (Zeros of a Polynomial) Suppose is a polynomial functions of degree Then,

    (i) there exists complex numbers such that

for some real number

    (ii)   has at most different complex zeros.
    
    (iii) if a zero of multiplicity is counted times, then has precisely zeros.

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Cite this as:
Zeros Of A Polynomial
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/zeros-of-a-polynomial.html