A polynomial of even degree (highest power of the variable is an even number) with real and complex zeroes will always have the latter in pairs. A polynomial with odd degree and some complex zeroes can only have them in pairs, and there must be an odd number of real zeroes. The reason is that each complex member of a pair must counterbalance its partner in order to produce real coefficients in the polynomial expression.
A simple example of a cubic polynomial is (x-i)(x+i)(x-1)=(x^2+1)(x-1)=x^3-x^2+x-1. The two complex factors complement one another.