What is the conjugate zeros theorem?

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Nov 16, 2015

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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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