I recently found WeBWork and was trying to write up some problems and wanted to make a problem such that the factors of the polynomial would have a pair of complex conjugates. I understand that $2$ is a complex number. I want to choose just those polynomials which will give $\mathbb{R}$ & an even number of $\mathbb{C}$ roots or just an even number of $\mathbb{C}$ roots. I do know that the coefficients must be rational numbers, but that is all. I believe there is something deeper for me to learn here.
How do I generate polynomials that do not have only real roots, with rational coefficients?
Thank you for your time.