.'.) ION 



turn of the roota, 

 \\L the rooU. 



the root* of a quadratic equation al , 

 li. uiselves needed, but f>nl\ their turn or t U de- 



i. these may be obtained directly from the given e< 

 ton 



.i the half sum of the roota of the equat 



r, are the roota of the equat 

 7-0, 



... r, ami r - factors of its first i 



r, hy i-| , this iMjiKitimi may be writ 



j^-f ^^-(^-l- =0, 



ami ^-(^ -hx,)^- + j-^j^l/- - *,), 



beoM * + />* + 7=(* ^ 



Conversely: if a quadrat ic funrtion can be separated i 

 t\M. :-, tlin the roots can be imiiu- 



-h 9=(x j-j)(r j-,), tluMi the first mem- 

 .vill van. >l nuly it", s f l = ' 



j* -f/wr 4- q = if x = j-j or r = x r 1 I x, an 



roots of the eqi: - + px + q = (. 



12. The quadratic equation involving two unknowns. One 



;:i involving t\\. unkiM>\\n nnniiKTs cannot be solved 

 uniquely ft tlu? values of those numbers which satisfy the 

 equation; i.ut if tliere is assigned to nth-r of th,.se num- 



