HP 35s Scientific Calculator - Manual (Page 324)

D-2 More about Solving
If f(x) has one or more local minima or minima, each occurs singly between
adjacent roots of f(x) (figure d, below).
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.
f (x)
x
a
f (x)
b
x
f (x)
x
c
f (x)
x
d
Function Whose Roots Can Be Found