The second states that if is a real polynomial not identically constant, then all
nonreal zeros of
lie inside the Jensen disks determined by all pairs
of conjugate nonreal zeros of (Walsh 1955, 1961; Householder 1970; Trott 2004, p. 22).
This theorem is a sharpening of Lucas's root theorem.
The third theorem considers a function defined and analytic throughout a disk and supposes that has no zeros on the bounding circle , that inside the disk it has zeros , , ..., (where a zero of order is included times in the list, and that . Then
, the function
(Cheney 1999).
is a real polynomial not identically constant, then all
nonreal zeros of 
lie inside the Jensen disks determined by all pairs
of conjugate nonreal zeros of 
(Walsh 1955, 1961; Householder 1970; Trott 2004, p. 22).
This theorem is a sharpening of Lucas's root theorem.
a function defined and analytic throughout a disk 
and supposes that 
has no zeros on the bounding circle 
, that inside the disk it has zeros 
, 
, ..., 
(where a zero of order 
is included 
times in the list, and that 
. Then
