IN THE HIGHER ALGEBRA, 133 
§ 7. 
Next, let (1) become 
which is equivalent to 
3 
(u— 1)°( 2? + 2u? + 8u+5 ) ==4 
or, if u«—1l=p, to 
15 
2 3 2 — 
(p+ 5p +10p+-")=0 pO Wibe. 6). 
Then, if g, 7 and s be the roots of 
5 
p+bpe+ lop +7 =0 j Piet tol LIA. (7), 
we have 
Lye tes — gees hate ee (PD (8) 
§ 8. 
For, since h is arbitrary, we may assume it equal to 
unity, and replace (4) by 
U=y(u-1) -5Q-10, 
a relation which, when (5) is satisfied, becomes 
25 
U=¥(p)-- ry 
But, by (6), two of the values of p are zero, and, therefore, 
v(p)=9"rs, 
and (8) is verified. 
§ 9. 
Permuting g, 7 and s in (8), and determining the sym- 
metrical functions by means of (7), we find that the six 
values of U are the roots of 
3 53 54 2 
{U+—- U-s} aif 
Consequently, by (2), the corresponding equation in @ is 
{ gs 3-5" y 5”)? _ 6 ( 
) ot “oz a" 915 et Ee Oy 6m St ake a) es (9). 
