HP 33s D–5, More about Solving D–5

	/	Checksum and length.
	/
‡		Cancels Equation mode.

Now, solve the equation to find its positive and negative roots:

Keys:	Display:	Description:
0 IX 10	_	Your initial guesses for the
		positive root.
H	%:-%. 	Selects Equation mode; displays
		the equation.
X	#	Calculates the positive root
	%/	using guesses 0 and 10.
	)
	)	Final two estimates are the
		same.
 )		f(x) = 0.
0 IX 10 ^	._	Your initial guesses for the
		negative root.
H	%:-%. 	Redisplays the equation.
X	#	Calculates negative root using
	%/	guesses 0 and –10.
	.)
 )		f(x) = 0.

Certain cases require special consideration:

„If the function's graph has a discontinuity that crosses the x–axis, then the SOLVE operation returns a value adjacent to the discontinuity (see figure a, below). In this case, f(x) may be relatively large.

„Values of f(x) may be approaching infinity at the location where the graph changes sign (see figure b, below). This situation is called a pole. Since the SOLVE operation determines that there is a sign change between two neighboring values of x, it returns the possible root. However, the value for f(x) will be relatively large. If the pole occurs at a value of x that is exactly represented with 12 digits, then that value would cause the calculation to halt with an error message.

More about Solving D–5