ABSTRACT
It is natural to start with polynomial equations whose coefficients are integers. The simplest case is the linear equation ax + b = 0, which has the root x = — £ € Q. Note that any linear equation with coefficients in a field F has its root in F, so we are led to consider equations with coefficients in a given field F. In general, since any root of a polynomial f (x ) is also a root of the polynomial obtained by dividing through by the leading coefficient of / , we might as well assume from the onset that / is monic.
