Editing Splitting field (section)

===Motivation===
Finding [[root of a polynomial|roots of polynomials]] has been an important problem since the time of the ancient Greeks. Some polynomials, however, such as {{math|''x''<sup>2</sup> + 1}} over {{math|'''R'''}}, the [[real number]]s, have no roots. By constructing the splitting field for such a polynomial one can find the roots of the polynomial in the new field.