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THEORY OF EQUATIONS. 



883. THE product of two unequal roots of the equation 



ax 9 + bx* + ex + d = 



is unity ; prove that the third root is ^ - . 



884. The roots of the equation x* - px + q = may be ex- 

 pressed in the forms 



Z 2 * , andp-? ? 

 P-P-P- *-!- 



Explain these results when p*<4q. 



885. If the equation x 3 px* + qx r = have two equal 

 roota, the third root must satisfy either of the equations 



x(x-p)' = 4r, (xp) (3x -I- p) + 4^ = 0. 



886. The roots of the equation x 3 px 9 + qx r = Q are the 

 sines of the angles of a triangle ; prove that 



8pr + 4r' = 0. 



887. Determine the relation between q and r necessary in 

 order that the equation x* qx -I- r = may be put into the form 



x* = (x* + mx 4- n) f ; 



uinl solve in this manner the equation 

 8x > -3G*+27=0. 



888. Find the condition necessary in order that the equation 



e > + fc 

 may be put under the form 



and solve by this method tin- 



z' + 3.c* + 4* -+-4 



