How do I use the conjugate zeros theorem?
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.)