Quadratic Equations on TI83/84
Copyright © 2004–2014 by Stan Brown, Oak Road Systems
Copyright © 2004–2014 by Stan Brown, Oak Road Systems
Summary: You can program your TI83/84 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 Jun 2008), unzip it to any convenient directory, and download it to your TI83/84.
Otherwise, you can enter the program manually. If you’re not familiar with TI83/84 programming instructions, please see the keystroke procedure in Entering the Program, below.
Disp "AX²+BX+C=0" Prompt A,B,C B²4AC→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 changesign 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
realonly mode. Select 1:Quit
.
You can set up your calculator to view nonreal 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 nonreal roots. The calculator remembers a+bi mode, like all modes, even when turned off.
See also: Complex Numbers on TI83/84
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 TI83/84 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
oneline 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 changesign 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 changesign 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 memorymanagement 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!
ALPHA
APPS
makes C
] to
[ALPHA
PRGM
makes C
], thanks to Rebekah PassThis page is used in instruction at Tompkins Cortland Community College in Dryden, New York; it’s not an official statement of the College. Please visit www.tc3.edu/instruct/sbrown/ to report errors or ask to copy it.
For updates and new info, go to http://www.tc3.edu/instruct/sbrown/ti83/