What is the conjugate zeros theorem?

1 Answer
George C.
Nov 16, 2015

If a polynomial has Real coefficients, then any Complex zeros will occur in Complex conjugate pairs.

That is, if z = a+bi is a zero then bar(z) = a-bi is also a zero.

Explanation:

Actually a similar theorem holds for square roots and polynomials with rational coefficients:

If f(x) is a polynomial with rational coefficients and a zero expressible in the form a+b sqrt(c) where a, b, c are rational and sqrt(c) is irrational, then a-b sqrt(c) is also a zero.

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