THEORY OF EQUATIONS. 191 



905. One of the roots of the equation 



is the square of another root ; explain why, on attempting to solve 

 the equation from the knowledge of this fact, the method fails. 



906. If a, ft y, 8, ... be the roots of the equation 



x" 

 then will 



= ( n - 1) (n - 2)p* - 3n (n - 2) Pl p t 



ami determine what symmetrical function of the differences of 

 the roots is equal to 



907. The equation x* - 209x -I- 56 = has two roots whose 

 product is 1 ; determine them. 



908. Prove that all the roots of the equation 



... to m + 1 terms = 



are real ; nnd that none lie beyond the limits and 1, n bring 



and m < n. 



900. Determine the integers between which lie the roots of 

 tbe equation 



/(*) = 12** 4- 16x f - 31* -1-10=0, 



having jjivrn /,(*) = 36af-- 32 - 31, 

 /.(*) = 3 13x- 197, 



/.(*) P fii 



