Eoss — Verh-Functions. 67 



For example, 



and so on. 



(5) Thus, consider the quadratic 



+ p^iX + p.2 = 0. 

 If we wish to obtain a single root by inverting the form 



X + p_oX~^ = - p_i, 

 then this will be possible only when is numerically greater than 

 4^.2 ; that is, when p-.i > 4^_2. 



If be positive and greater than ip^i, the series becomes divergent, 

 and at the same time the root becomes unreal. If jt?-2 be negative and 

 numerically greater than i^^^.i, the series is divergent though the root 

 is real. In this case, however, both roots can be obtained at once by 

 operative division from the form 



+ P-iX = - P.O. 



The same condition holds with regard to any trinomial equation 

 x'' + p^,x"~'' + = 0. 



Take 



x^ + lOx^ + 2 = 0. 



Here p-i = 10, and p--^ = 2 ; and obviously 10 is the predominant 

 coefficient, because 



We can, therefore, obtain a single root from the form 

 X + 2x^-^ = - 10 



