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BOOK OP MATHEMATICAL PROBLEMS. 



910. Determine the integers between which lie the real foots 

 of the equation 



5 - Wx a - I5x a -6x-Q = 0. 



911. Find the sum of the n ih powers of the roots of the equa- 

 tion x* x 8 + 1 = ; and form the equation whose roots are the 

 squares of the differences of the roots of the given equation. 



912. If s r denote the sum of the r ih powers of the roots 

 of the equation 



x n + Pl x n -*+p^-> + ...+p n = Q, 



and S m = s l + s a + ... + s m prove that, if S m have a finite limit 

 when m is indefinitely increased, that limit is 



" 1 is divisible 



is divisible 



913. The integer next less than ^ (J3 + 

 by 2 n , n being integral. 



914. The integer next greater than (x/3 

 by 2'". 



915. The roots of the equation 



x s - Pl x 4 + p a x a -p a x a +p<x-p 6 = 

 exceed those of the equation 



x 6 - qp* + ? 2 ce 8 - qjt + qp-q^ 

 respectively by the same quantity ; prove that 



fa - *Pri - 5Qp I p 4 + 5p aPa + 



