A study on some of the contributions of Albert Girard in Algebra

  • Joyce Kurian Research Scholar, Research and Development centre, Affiliated to Bharathiar University, Coimbatore-641046
  • Sunny Joseph Kalayathankal Associate Professor, Dept. of Mathematics, K.E.College (Affiliated to Mahatma Gandhi University), Mannanam, Kottayam, Kerala-686561
Keywords: Fractional exponent, Power, Root, Negative solution, Quantity, Factions

Abstract

             Albert Girard introduced the notion of a fractional exponent, “the numerator is the power and the denominator the root” and the current notation for higher roots. He understood the geometric meaning of a negative solution to an equation. He generalized the work of Viete and considered ‘factions’, which are the elementary symmetric functions of n variables. He also noted the Pascal triangle of binomial coefficients. He identified the relationships that exist between the roots of an algebraic equation and the coefficients that appear in the equation itself. He found that every algebraic equation admits of as many solutions as the denomination (power) of the highest quantity indicates. He preferred arranging equations in alternating order of decreasing degree on each side of an equation. This arrangement helped him to state the relation between coefficients and roots. His hypothesis that, every polynomial equation has a number of solutions equal to its degree was his most interesting contribution.

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