Theory of Quadratics. 65 



stituted for x, cause the function of x to vanish. For the func- 

 tion of X is 



-T^— 3Jf— 10 

 and putting 5 for x it becomes 



25—15—10 

 which is zero. Putting — 2 for ;f the function of x becomes 



4+6—10 

 which is also zero. 



If anything else than a root is put for x the function will not 

 vanish ; thus when 



-r=— 4, function of x becomes 16+12—10= 18 



9+ 9-10= 8 

 4+ 6-10= o] 

 1+ 3-10=- 6 • 

 0+ o-io=-io 



I- 3-IO=-I2 



" " ** 4— 6— io= — 12 



" " " 9— 9—10= — 10 



" " " 1,6—12—10=— 6 



25—15—10= o] 



36-18-10= 8 



2. If we suppose the quadratic function divided through by 

 the coefficient of x" it may be represented by 



x^^-ex-\rf. 

 If we take the quadratic x^+px=q, and transpose the q to the 

 other side of the equation, we obtain 



x''-]rpx—q=o 

 where the left member is seen to be of the form x^-\-ex-{-f. Then, 

 since every quadratic may be put in the form x--\-px=q, it may 

 also be placed in the form 



x^-^px—q=o 

 or better x^-\-ex-\-/=^o. 



In either of the quadratic functions 



lx--\-7ix-\-r 

 or x~-\-cx+f 



the term which does not contain x, that is r or /, is called the ab- 

 solute term. 



