The Moduli of the Roots of an Algebraic Equation
Elizabeth Beaman · American Mathematical Monthly · 1946
(3) m(r) = IaIr2(V/2V b2acI +I b+ Iacj )r+IcI. Finding g(n) for the cubic is reduced to the problem of finding ,Nz for the reduced cubic. The value ZNz for the reduced cubic is one of the roots of a specified cubic. The general case is not completely treated. The polynomial g(n) for an equation of degree m is shown, however, to be a factor of a polynomial R(n) whose degree is m2. As a by-product, there is found a method for obtaining the equation of degree mp, whose roots are the products of the m roots of a polynomiaJ f(z) by the p roots of a polynomial g(z).