421 
equal Roots of an Equation by Di-vifon. 
He re ^=-0, ^ = — 9, r~ ~ 4, andj=i2; and 
A becomes = 
B . . = 
C . . = 
12X -4 _ 
-8 x -9 3 ’ 
—16 x — 12 — 8 
- 8 x~' 9 ~ ~ 5 
4 X Y+ l8 
4X 1 
4 
D 
and 
5 * 
D-B- 
- Zi- 
— 1 s = 
j > 
t+T 18 + 32 50 _ 
, ,, — n ~ 2 » 
A-C “z 2 -pH “ -8 + 33 25 
4 
which being written for a*, the equation becomes 16 — 364- 81 
+ 12 = 0; therefore 2 is one of the roots. 
The fame value of a;, may be. difcovered from either of the 
quadratic equations mentioned in corollary 1. The proper values 
of the co-efficients being written in the firft of them, it becomes 
,v s - - x — ? = o, where one value of x is — ^ =• 2. The 
3 3 3 
other quadratic becomes y 1 — — y + | = o, one of whole roots is. 
IX+i/ 25 _ „ 
8 
EXAMPLE II. 
It being known that the equation v 4 - - jx z -f 1 3* - 6 = o 
has two equal roots, to find them. 
Here /> = 1 , <7 = - 7, r- - 13, and j = ~ 6 ; and A = 
— 142 t> __ 83 p _ — 1 
59 1 ’ '" 59 ’ 39 1 
12800 j D-B 12800 
and 
D= — , D - B = a-C 
39 1 23009 
23069 : 
A-C 12800 
= i, one of the roots fought. 
The 
