HP HP-32S - When SOLVE Cannot Find a Root

When SOLVE Cannot Find a Root
Sometimes SOLVE fails to find a root. The following conditions cause
the message NO ROOT FND:
• The search terminates near a local minimum or maximum (see fig
ure a, below). If the ending value of /fa)(stored in the Z-register) is
relatively close to zero, it is possible
mat a root has been found; the
number stored in the unknown variable might be a 12-digit
num
ber very close to a theoretical root.
• The search halts because
SOLVE is working on a horizontal asymp
tote—an area where /fa)is essentially constant for a wide range of x
(see figure b, below). The ending value of /fa) is the value of the
potential asymptote.
• The search is concentrated in a local 'flat* region of the function
(see figure c, below). The ending value of /fa) is the value of the
function in this region.
fix)
fCxJ
fCxJ
•»• X
Cases Where a Root Is Not Found
C: More About Solving an Equation 267