Of CUBIC EQUATIONS. 109 



The following examples are chiefly taken from Dr Hut- 

 ton's " TraSts Mathematical and Philofophical." Trafi 5. 

 11. Example i. Let the propofed equation be 

 x l — 6x z + 1 ix — 6 ~ o. 

 Here, A = — 6, B rr: -f 1 * > C — — 6: therefore 



M = + 2 

 N =— 2 

 m = -f- 14 

 » = + 6 



Q = -4 



So that we have here Cafe I. 



14 7 



and T = V^L It 



CO 



Now, tan 90°= 00 , and alfo tan 270 = co : And we may take- 

 either of thefe angles for <p : Take <p zz 90 °, then, 



2=tan 3 o- = + ^ 



z = tan - = tan io° = -f- 

 3 J 



2 = tan ^+120°) =rtani5o°=— tan3o°=:— --^r 

 ^ — tan ^-j-240 ) = tan 270° = co 



-L 4. JL 

 Therefore,* =r ■" 5li = - = ^ 



^ + 7i 4 



_r £_ 



x = ^ ^= 6 ~= % 



. 1 2 J 



And fo the three roots are 1, 2, and 3. • 



Since 



