390 Dr. hutton on Cubic Equations 
transform every cubic equation before we attempt the 
refolution of it. 
4. Let therefore x z + px - q be fuch a cubic equation 
wanting the fecond term, where p and q reprefent any 
numbers, pofitive or negative. 
5. Now from the premifes it follows, that this equa- 
tion has three roots ; that fome are pofitive, and others 
negative ; that two of them are of one affedtion, and are 
together equal to the third of a contrary affection, 
namely, either two negative roots, which are together 
equal to the other pofitive, or two pofitive roots equal to 
the third negative. 
6. But the figns of the three roots are eafily known 
from the fign of the quantity q ; the fign of the greateft 
root being the fame with the fign of q when this quan- 
tity is on the right-hand fide of the equation, and the 
other two roots of the contrary fign. For when q is on 
the fame fide of the equation with the other terms, it has 
been obferved, that it is always equal to the continual 
produdt of all the roots with their figns changed ; confe- 
quentlv q is equal to the product of all the roots under 
their own figns, when that quantity is on the other or 
right-hand fide of the equation : but the product of the 
two lefs roots is always pofitive, becaufe they are of the 
fame affediion, either both + or both - ; and therefore 
1 this 
