ABSTRACT
Polynomials have played a major role in the study of algebra and geometry. Even before the time of Euclid, Babylonians (586 B.C.) knew that a right-angled triangle with legs each of unit length must have a hypotenuse √2 units in length. (The ancient Babylonian Empire was situated in Euphrates valley about 100 kms south of Baghdad (Capital of Iraq which was formerly known as Mesopotamia). Pythagoras (580–500 B.C.) is known by the theorem that bears his name, although the theorem was known to Babylonians. It is reported that Egyptians were familiar with methods of solving polynomial equations in special cases. From the time of Hippocrates (c. 460 B.C.) till the time of Diophantos (c 250 A.D.), Greeks attempted numerical problems which could be stated in terms of polynomials. In Greek algebra, magnitudes were represented by line segments and the problem of nding the roots of a quadratic equation meant a solution in the form of a straightedge and compass construction for line segments representing the roots. By 1100 A.D., Arabs developed algebra to the extent where they were conscious of tackling cubic equations. In the sixteenth and seventeenth centuries, methods of nding the roots of a quadratic, cubic and biquadratic equations were found out in the form of ‘formulae for roots’. The contributions of Euler, Lagrange, Niels Henrik Abel (1802–1829) and Everiste Galois (1811–1832) to the ‘insolvability of the quintic’ are well-known. As mentioned in chapter 3, when Rene Descartes (1596–1650) invented analytic geometry, the door was opened for a fusion of ideas of Calculus which unfolded itself at the hands of Newton and Leibnitz.
