420 Mr. hull INS* s Method oj finding the 
as the co-efficients of. it, are lefs complex than thofe of the 
other v 
%pp — 8 ^ x x* -f 1 2r - 2 pq x a: +pr — 1 6s s o, 
and 4A + 3/ * a 1 + 4B-- zq x x + r~o. And* thdc,-. 
when p = o, become -±$qx* 4-. 1 2™ 1 6s q, 
and -^ + ^'_ 2? x.v + r = o, i . 
a V , 2J 
or x — - a -f = o, 
2 ? f 
and a 2 + - - = Oi 
3 r 6 
corol, .2. If both p and 7 vanifh, then, from either of the 
quadratics we. get x=±I, perfe&ly agreeing with the cubic. 
px z — 2^a 2 41 s o, which, when p and ^ vanifh,. becomes 
3 rx — 45 = o. And this equation is of ule; becaufe, in . this 
cafe, the theorem fails, one of* the divifors being :no. 
♦ 
corol. 3. From the equation 4A 3 — $px z 4* 2qx — r — o, which, 
when ^ and q vanifli, becomes 4* 3 -r=_o, we alfo get 
~ - ? another expreffion of the fame value of a. 
corol. 4, When r=o, D~o, and from the equation 
x 1 + Ca + D=: o, we have x = - C. 
EXAMPLE I. 
If the equation * * * - p.r + 4 a + 1 2 = o has equal roots, it is 
propofed to find them. 
Here 
