Polynomial Zeros

Theorem (Polynomial Zeros) Conjugate Pairs Theorem. If a polynomial of degree has real coefficients and if with is a complex zero of then the conjugate is also a zero of

Theorem (Polynomial Zeros) Rational Roots Theorem. If the polynomial



has integer coefficients and if is a rational zero of such that and have no common prime factor, then

    (i) the numerator of the zero is a factor of the constant term
    
    (ii) the denominator of the zero is a factor of the leading coefficient

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