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# HP 50g Graphing Calculator - Solving for Zeroes of a Function

## The numeric solver

The HP 50g has a numeric solver that can find the solutions to many different types of problems. It is invoked by pressing the
ORANGE shift key followed by the key, or

When pressed, the CHOOSE box below is displayed:

**Figure : Displays the CHOOSE box**

The first choice allows for the solution of an equation containing a number of unknowns. The second choice solves differential
equation problems. The third choice solves for zeroes of a polynomial and is of interest here. The fourth choice can solve linear
systems of equations for unknown values. The fifth choice invokes the finance solver. The sixth choice begins the multiple equation
solver. To select the equation solver, press . The 50g displays the following screen:

**Figure : Displays the solve equation screen**

There is one input area on this form. This is where equation to be solved is entered. To enter an equation, press .

**Figure : Entering the equation**

The cursor will be flashing between the two quote marks at the bottom left corner of the screen. The 50g is waiting for the entry of an
equation. Type in the following:

**Figure : Entering the equation**

and press shown above the key at the right side of the display. The equation entered will be stored in the variable EQ in
the current directory and will be displayed in the Eq: line of the screen, as shown below. If the variable EQ already contained an
equation when the solver was entered, it would have been displayed in the Eq: line in the display above.

**Figure : Displays the equation**

If you prefer, the EquationWriter can be used to type an equation which is then placed on the stack. If you place the ‘EQ’ name in the
first level of the stack with the equation from the EquationWriter in the second level of the stack and press , the equation will be
stored in the EQ variable. It may be easier to do this before starting the solver for many equations.

The remainder of the screen below the Eq: line is where the 50g solver will place variables found in the equation. Each variable will
be given an input space on this screen where you can either input a known value for the variable or attempt to solve for the value of
that variable if it is unknown. In the example shown, the only variable is X and there is one entry line for it as shown below.

**Figure : Displays the equation**

To solve for the value of X that makes the entered equation equal to zero, press the menu label above the key at the
right side of the display. The 50g will solve for X and return its value as shown below.

**Figure : Displays the value for X**

Note that the solver returned only one of the real solutions to the equation, +2. The solver only finds one answer. To seek for other
answers, a starting guess can be given for the variable to influence the search for an answer. It may also be easier to graph the
function and look for roots in that manner. Consider what the solver returns if the cursor is placed over the X: input area and –3 is
entered followed by pressing the menu label above the key at the right side of the display:

**Figure : Displays the value for X**

The solver found the other real solution to the equation. If you do not have any idea for a possible solution, the solver will make a
guess and attempt to find an answer. However, to find other answers, a user-supplied guess may be needed.

**Figure : Displays the real solution to the equation**

## Practice finding zeroes of a function

### Example 1

What are some values of X for which the equation below has a value of zero?

### Solution

To find some of these X values, use the EquationWriter to enter the function and solve for a root using the numeric
solver as shown.

**Figure : Entering the values**

**Figure : Entering the values**

**Figure : Entering the values**

**Figure : Displays the values**

(This is one value of X for which the function’s value is zero)

**Figure : Displays the values**

### Answer

Two of the values of X for which the function has a value of zero are approximately 0.92945 and –1.01264. It might
be easier to find all of the values of X that will produce a value of zero for this function by plotting this equation and
seeking the roots graphically. This is covered in another training aid.

### Example 2

What are some values of X for which the equation below has a value of zero?

**Figure : Entering the values**

### Solution

To find some of these X values, use the EquationWriter to enter the function and solve for a root using the numeric
solver as shown.

**Figure : Displays the equation**

**Figure : Entering the value for X**

(This is one value of X for which the function’s value is zero) .

**Figure : Entering the value for X**

(This is another value of X for which the function’s value is zero)

### Answer

Two of the values of X for which the function has a value of zero are –3 and 4. It might be easier to find all of the
values of X that will produce a value of zero for this function by plotting this equation and seeking the roots
graphically. This is covered in another training aid.

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