# How do I use the conjugate zeros theorem?

##### 1 Answer

**As a student,** if a teacher tells you that a polynomial with real coefficients has

With real corrifients, if

So I know that

**I saw this** interesting bit of reasoning recently here on Socratic.

We know that a polynomial of degree

We also know that if a polynomial has real coefficients, the any imaginary zeros occur in conjugate pairs.

So we can conclude that a polynomial with real coefficients and odd degee must have at least one real zero. (An odd number of zeros cannot all be imaginary.)