happysharlee
Junior Member
USA
5 Posts 
Posted  01/17/2011 : 11:02:19

P(x) = x^4  6x  x + kx  72; x2 is a factor
So, I used synthetic division and got k=54, and I reduced the polynomial to x  4x + 54x 72.
By Des Cartes theorem, there should be one other positive root and one negative root.
By the conjugate roots theorem, the possible roots are 72, 36, 24, 18, 12, 9, 8, 6, 4, 3, 2, 1.
I tried to find the Upper/Lower bounds and got 4 as the lower bound and 6 as the upper bound. Am I doing something wrong? nothing seems to be divising out to 0, if that makes sense? 
Edited by  happysharlee on 01/17/2011 15:56:00 

