HP 32SII Owner's Manual page 316

If f(x) has one or more local minima or minima, each occurs singly
between adjacent roots off f(x) (figure d, below).
f (x)
a
f (x)
c
In most situations, the calculated root is an accurate estimate of the theoretical,
infinitely precise root of the equation. An "ideal" solution is one for which f(x)
= 0. However, a very small non–zero value for f(x) is often acceptable
because it might result from approximating numbers with limited (12–digit)
precision.
C–2 More about Solving
File name 32sii-Manual-E-0424
Printed Date : 2003/4/24
x
x
Function Whose Roots Can Be Found
Size : 17 .7 x 25.2 cm
f (x)
b
f (x)
d
x
x