398 Dr. hutton on Cubic Equations 
a 8. Hence then in an eafy and general manner we 
can reprefent any form or cafe of the general equation, 
with all the circumftances of the roots, by only taking, 
in thefe laft formulae, any particular number for », either 
pofitive or negative, integral or fractional, &c. As if 
n— 1 ; then the equation becomes x l - r* x = or = o, 
the value of e - \r. the root r-\/p- 3 /ii = , and the 
z 7 £ V o op 
other two roots and - \r. o = - r 
and o. 
eg. If n — — 1, the equation will be x 3 — x — |r 3 , the 
value of e — \rV- 1, the root r = | = V ip — 2 q> and 
the other two roots = - \r . 1 ± \/ 1 imaginary. 
30. And thus, by taking feveral different values of n, 
pofitive and negative, the various correfponding circum- 
ftances and relations of the equation and roots will be 
exhibited as in the following table. 
Forms 
