• The fundamental theorem of algebra states that in the field of complex
numbers every polynomial equation has at least one root.
As a consequence of this theorem, it can be proved that every nth degree
polynomial has n roots in the complex field. When complex numbers are
admitted, the polynomial theoretically may be expressed as the product of
n linear factors; with our restriction to real numbers, it is possible that 2k of
the roots may be complex. In this case, the k factors generating them will
be quadratic.
