ALGEBRA 



or: 



01 



Sl= -- 



202 0i 

 = --- 1 -- 5 



_ 303 



" 0o 2 0o 3 



_ 4f*4 40133 _ 4fll 2 fl2 202 2 0i* 



do ao 2 0o 3 0o 2 0o 4 



1.205 If Sk denotes the sum of the reciprocals of the &th powers of all the 

 roots of the equation f(x) = o : 



&-V-1+ +A 



Ci* C 2 k C n k 



Idn-l + Sld n = O 



- O20n == O 



- O2071 1 ~1~ OS071 O 



d n -l 



01 = -- 



. 

 02 = --- 1 



0n 0, 



1.220 If f(x) is divided by x - h the result is 



/(*) -...(*- WQ + R. 



Q is the quotient and R the remainder. This operation may be readily per- 

 formed as follows: 



Write in line the values of a , <*i, . . . ., a n . If any power of x is missing 

 write o in the corresponding place. Multiply do by h and place the product in 

 the second line under a\\ add to a\ and place the sum in the third line under a\. 

 Multiply this sum by h and place the product in the second line under 02; add 

 to 02 and place the sum in the third line under 0%. Continue this series of 

 operations until the third line is full. The last term in the third line is the 

 remainder, R. The first term in the third line, which is do, is the coefficient of 

 x n ~ l in the quotient, <2; the second term is the coefficient of x n ~ 2 , and so on. 



