Question

What is the conjugate zeros theorem?

Answer 1

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.