ALGEBRA. 1 ."i 



III. Theory of Quadratic Equations. 



79. In the equation 



abed 



4- r +- - = 0, 



x nul x mc x + mb x + ma 

 pn ve that, if a4&4C46?=0, the only finite value of x will be 



W) 



a + b 



80. In the equation 



x + 6, 



* -V 



prove that, if 



a, 4 b t 4 a 9 4 a 4 = 0, and a l b l 4 aj> t 4 a a 6 8 4 a 4 5 4 - 0, 

 the only finite value of x will be 



CL O ~^* (I f) ~^ & O * *\ 



A'..A'.^ A'.^A-. - ( J . + *. + 6 - + > 



81 . Fiml limits to the real values of x and y which can satisfy 

 the equation 



4- 



82. If the roots of the equation 



ax 9 4 2foe 4 c 

 be powible and different, the root* of the equation 



will l>e iiniKxwible, and vice twvtf. 

 83. Prove that the equations 



x + y4*-a4&4-c, 



?4^4* 1, 



a 6 c 



are equivalent only to two i i t ' - 4 j 4 - - 0. 



