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  • 1. TC3 → Stan Brown → TI-83/84/89 → Quadratic Equations revised 30 Nov 2009 (What’s New?) Quadratic Equations on TI-83/84 Copyright © 2004–2012 by Stan Brown, Oak Road SystemsSummary: 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 ProgramThe 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 ile (13 KB,revised 22 Jun 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‐83/84programming 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 DRunning the ProgramTo run the program, press [PRGM]. Look at the list of programs and press the appropriate number; orscroll to the program and press [ENTER]. The program name will appear on your screen. Press [ENTER] torun it.Example: you know that x²−5x+6 = 0 factors as (x−2)(x−3) = 0, andtherefore 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 1 of 5
  • 2. 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 isintended for checking your calculations; you’ll still be expected to solve quadratic equationsmanually in class and in homework. Complex RootsIf you get the message “NONREAL ANS” when running the program, itmeans your equation has no real roots but your calculator is in real‐onlymode. Select 1:Quit. You can set up your calculator to view non‐realroots, 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 ind the roots 2±3i.Entering the ProgramProgramming the TI‐83/84 isn’t hard, but it does use a bunch of keys and menus you might not befamiliar with. Just type everything exactly as shown, and check the display as you go along. Don’t pressthe [2nd] or [ALPHA] key unless the instructions tell you to, and do be careful not to use one in place ofthe other. I recommend ticking off each step with a pencil as you do it, so that you don’t get lost. 2 of 5
  • 3. Open the Program Editor for a new [PRGM] [◄] [ENTER]program.Enter a name for the new program, such You’re already in alpha mode. Use the little green letters, andas QUADRAT. press [ENTER] when inished.optional: Any good program should give For Disp, press [PRGM] [►] [3].some idea what it’s doing. This one‐linecomment should be instantly Press [ALPHA + makes "].recognizable to anyone who has studiedquadratic equations. The line you are Press [ALPHA MATH makes A] [x,T,θ,n] [x²] [+].creating is Disp "AX²+BX+C=0" Press [ALPHA APPS makes B] [x,T,θ,n] [+].However, if you want to leave out thisdocumentation step the program will Press [ALPHA PRGM makes C].still run. For the = sign, press [2nd MATH makes TEST] [1], then inish the command with [0] [ALPHA + makes "] [ENTER]. Notice that the command wraps automatically to the next line.Now program the instructions to ask for For Prompt, press [PRGM] [►] [2].the coef icients A, B, and C. 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 famousquadratic formula,Start with the discriminant B²−4AC, [ALPHA APPS makes B] [x²] [−] [4] [ALPHA MATH makes A] [ALPHA PRGMwhich determines whether the roots makes C] [STO→] [ALPHA x-1 makes D] [ENTER]are real. To save typing later, you willcompute it and store it in a newvariable, D. 3 of 5
  • 4. Now compute and display the two [PRGM] [►] [3] [(] [(-)] [ALPHA APPS makes B] [+] [2nd x² makes √]roots. [ALPHA x-1 makes D] [)] [)] [÷] [(] [2] [ALPHA MATH makes A] [)]The irst root is (−B+√(D))/(2A). Be [ENTER]sure to use the change‐sign key [(-)]and not the minus key [−]!The second root is nearly the same, [PRGM] [►] [3] [(] [(-)] [ALPHA APPS makes B] [−] [2nd x² makes √](‐B−√(D))/(2A). Be sure to use the [ALPHA x-1 makes D] [)] [)] [÷] [(] [2] [ALPHA MATH makes A] [)]change‐sign key [(-)] for the irst “‐” [ENTER]and the minus key [−] for the second! 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. The DelVar command is on the PRGM menu.Though they don’t take up much space, [PRGM] [ALPHA TAN makes G] [ALPHA MATH makes A] [ENTER]if left in memory they’ll surprise you on [PRGM] [ALPHA TAN makes G] [ALPHA APPS makes B] [ENTER]the memory‐management screen. [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!What’s New 1 Dec 2009: correct [ALPHA APPS makes C] to [ALPHA PRGM makes C], thanks to Rebekah Pass 22 Jun 2008: add a PDF of the program to the download ile 5 Aug 2007: clarify and simplify TI‐83 keystrokes (intervening changes suppressed) 25 Jan 2004: new document and TI‐83 program 4 of 5
  • 5. This page is used in instruction at Tompkins Cortland Community College in Dryden, New York; it’s not an of icialstatement 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/ 5 of 5