# What is the conjugate zeros theorem?

##### 1 Answer
Nov 16, 2015

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

That is, if $z = a + b i$ is a zero then $\overline{z} = a - b i$ is also a zero.

#### Explanation:

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

If $f \left(x\right)$ 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.