Quadratic Equations on TI-83/84

Summary: You can program your TI-83/84 to solve quadratic equations, and this page shows you the procedure. Though you need to know how to solve quadratics by the methods taught in class, the program is a great way to check your work for accuracy.

The Program

The program below solves a quadratic equation whether it has real roots or not.

If you have the TI Graph Link software, you can download the program from this ZIP file (13 KB, revised 22 June 2008), unzip it to any convenient directory, and download it to your TI-83/84.

Otherwise, you can enter the program manually. If you’re not familiar with TI-83/84 programming instructions, please see the keystroke procedure in Entering the Program, below.

Disp "AX²+BX+C=0"
Prompt A,B,C
B²-4AC→D
Disp (-B+√(D))/(2A)
Disp (-B−√(D))/(2A)
DelVar A
DelVar B
DelVar C
DelVar D

Running the Program

To run the program, press [PRGM]. Look at the list of programs and press the appropriate number; or scroll to the program and press [ENTER]. The program name will appear on your screen. Press [ENTER] to run it.

Example: you know that x²−5x+6 = 0 factors as (x−2)(x−3) = 0, and therefore the roots are 2 and 3. Run the program with A=1, B=−5, C=6. (Be careful to use the change-sign key [(-)] and not the minus key [−].) The answers 2 and 3 are produced, as expected.

Example: 25x²−20x = −4. First put it in standard form, 25x²−20x+4 = 0. Now run the program with A=25, B=−20, C=4. You see roots of .4 and .4, a double root of 2/5. This makes sense because the equation factors as (5x−2)² = 0.

Try additional examples using equations in your textbook. Remember that the calculator program is intended for checking your calculations; you’ll still be expected to solve quadratic equations manually in class and in homework.

Complex Roots

If you get the message “NONREAL ANS” when running the program, it means your equation has no real roots but your calculator is in real-only mode. Select 1:Quit. You can set up your calculator to view non-real roots, as follows:

You want to select a+bi mode.

Press [MODE] [▼ 6 times] [►] [ENTER].   Return to the home screen with [2nd MODE makes QUIT].

You can now run the program again to view the non-real roots. The calculator remembers a+bi mode, like all modes, even when turned off.

See also: Complex Numbers on TI-83/84

Example: −x²+4x = 13. First put the equation in standard form: −x²+4x−13 = 0. Then run the QUADRAT program with A=−1, B=4, C=−13 to find the roots 2±3i.

Entering the Program

Programming the TI-83/84 isn’t hard, but it does use a bunch of keys and menus you might not be familiar with. Just type everything exactly as shown, and check the display as you go along. Don’t press the [2nd] or [ALPHA] key unless the instructions tell you to, and do be careful not to use one in place of the other.

I recommend ticking off each step with a pencil as you do it, so that you don’t get lost.

Open the Program Editor for a new program.	[PRGM] [◄] [ENTER]
Enter a name for the new program, such as QUADRAT.	You’re already in alpha mode. Use the little green letters, and press [ENTER] when finished.
optional: Any good program should give some idea what it’s doing. This one-line comment should be instantly recognizable to anyone who has studied quadratic equations. The line you are creating is      Disp "AX²+BX+C=0" However, if you want to leave out this documentation step the program will still run.	For Disp, press [PRGM] [►] [3].   Press [ALPHA + makes "].   Press [ALPHA MATH makes A] [x,T,θ,n] [x²] [+].   Press [ALPHA APPS makes B] [x,T,θ,n] [+].   Press [ALPHA PRGM makes C].   For the = sign, press [2nd MATH makes TEST] [1], then finish the command with [0] [ALPHA + makes "] [ENTER]. Notice that the command wraps automatically to the next line.
Now program the instructions to ask for the coefficients A, B, and C.	For Prompt, press [PRGM] [►] [2].   Press [ALPHA MATH makes A] [,] [ALPHA APPS makes B] [,] [ALPHA PRGM makes C] [ENTER].

At this point your screen should look exactly like the one above. The next step is to compute the famous quadratic formula,

Start with the discriminant B²−4AC, which determines whether the roots are real. To save typing later, you will compute it and store it in a new variable, D.	[ALPHA APPS makes B] [x²] [−] [4] [ALPHA MATH makes A] [ALPHA PRGM makes C] [STO→] [ALPHA x-1 makes D] [ENTER]
Now compute and display the two roots. The first root is (−B+√(D))/(2A). Be sure to use the change-sign key [(-)] and not the minus key [−]!	[PRGM] [►] [3] [(] [(-)] [ALPHA APPS makes B] [+] [2nd x² makes √] [ALPHA x-1 makes D] [)] [)] [÷] [(] [2] [ALPHA MATH makes A] [)] [ENTER]
The second root is nearly the same, (-B−√(D))/(2A). Be sure to use the change-sign key [(-)] for the first “-” and the minus key [−] for the second!	[PRGM] [►] [3] [(] [(-)] [ALPHA APPS makes B] [−] [2nd x² makes √] [ALPHA x-1 makes D] [)] [)] [÷] [(] [2] [ALPHA MATH makes A] [)] [ENTER]

At this point, carefully check your screen against the screen shot at left. Be particularly careful about the two minus signs and the proper numbers of parentheses.

If you see any differences, cursor to the mistake and correct it. Remember you can use [2nd DEL makes INS] to insert characters so that you don’t have to retype a whole line. After making your corrections, move the cursor back to the empty line at the bottom.

optional: Delete the created variables. Though they don’t take up much space, if left in memory they’ll surprise you on the memory-management screen.

The DelVar command is on the PRGM menu. [PRGM] [ALPHA TAN makes G] [ALPHA MATH makes A] [ENTER] [PRGM] [ALPHA TAN makes G] [ALPHA APPS makes B] [ENTER] [PRGM] [ALPHA TAN makes G] [ALPHA PRGM makes C] [ENTER] [PRGM] [ALPHA TAN makes G] [ALPHA x-1 makes D] [ENTER]   Leave the program editor by pressing [2nd MODE makes QUIT].

If you’ve done everything right, your program is now ready for testing!