Quadratic Equations on TI-83/84
Copyright © 2004–2017 by Stan Brown
Copyright © 2004–2017 by Stan Brown
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 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
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.
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
You can set up your calculator to view non-real roots, as follows:
|You want to select a+bi mode.
Return to the home screen with [
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.
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
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.||[|
|Enter a name for the new program, such as QUADRAT.||You’re already in alpha mode. Use the little green letters, and
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
However, if you want to leave out this documentation step the program will still run.
|Now program the instructions to ask for the coefficients A, B, and C.||For |
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.||[|
|Now compute and display the two roots.
The first root is (−B+√(D))/(2A). Be sure to use the change-sign key [
|The second root is nearly the same,
Be sure to use the change-sign key [
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 [
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
|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 |
Leave the program editor by pressing [
If you’ve done everything right, your program is now ready for testing!
C] to [
C], thanks to Rebekah Pass.
Updates and new info: http://BrownMath.com/ti83/