β’ 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.
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