loS ^ NEJV SOLUTION ■ 



I. Compute, M — 3 + 2A + B 

 N =:A + 2B + 3C 

 mzzBN — 3CIVI 

 ti — ^N — AM, 

 And Q= (4B' + 270=) — 2AC (9B — A^-) + A' (2 AC — BO 

 And let it be carefully noted under which of the two follow- 

 ing cafes the equation comes : 



Case I, When QJs negative. 

 Case II. When Q^is pofitive. 

 To thefe two cafes a third may be added, viz. when Qj= o : 

 but of this cafe I iliall treat in one of the following examples. 



2. Compute alfo, a zz ,~-"'r^ 



3. Then, if the equation comes under cafe I : Find the an- 

 gle (p, of which the tangent is r, the radius being unity : take 



z =: tan|,z r: tan (^ + 120°), and z = tan (^ + 240°) : And 



the three roots of the equation will be found, by fubftituting 



thefe values of z in the formula x =. f^^' 



4. But if the equation comes under Cafe II. we muft com- 

 pute 



And the only root of the equation will be found, by fubftitu- 

 ting this value of z in the formula x =. jjT^* 



The 



