How to Use the Polynomial Root Finder on the TI-84 Evo

The TI-84 Evo has a Polynomial Root Finder built in, one of the apps on the grid that opens when you press on. Hand it the coefficients of a quadratic, or of anything up to order 10, and it lists every root at once, often as an exact fraction instead of a rounded decimal.

Open the Polynomial Root Finder

  1. Press on for the app grid, and arrow onto the p(x)=0 icon. The bar along the top names whatever is highlighted, so it reads POLYNOMIAL ROOT FINDER when you have the right one. If the icon isn't on your grid at all, a full memory reset has removed it along with the other built-in apps, and restoring your missing apps puts it back.
    The TI-84 Evo app grid with the p(x)=0 icon highlighted and POLYNOMIAL ROOT FINDER named in the title bar
  2. Press enter to open it. The app starts on a SETUP screen. ORDER is the highest exponent in your equation. The highest exponent in a quadratic is the 2 from x², so it can stay on 2.
    The TI-84 Evo Polynomial Root Finder SETUP screen with ORDER set to 2
  3. Press NEXT. The five labels along the bottom of the screen belong to the five keys on the top row, which carry the green f1 to f5 markings. NEXT sits above graph, so that is the key that moves you on.
    The TI-84 Evo top row of keys with the graph key highlighted
    The TI-84 Evo Polynomial Root Finder coefficient screen showing 1x squared plus 0x plus 0 equals 0

Type the coefficients and solve

The coefficient screen is the whole app. This walk-through solves 2x² + 3x − 2 = 0.

  1. Type the first coefficient. Press 2. It lands on the entry line at the bottom of the screen while the box itself still shows its old value, which is what you should expect. Press enter and the 2 drops into the box, and the highlight moves onto the sign just after the term.
    The TI-84 Evo Polynomial Root Finder with 2 entered as the leading coefficient and the plus sign highlighted, prompting Press plus or minus
  2. Set that sign. The signs between the terms are boxes of their own, and the prompt at the bottom spells out what they take: Press [+] or [-]. That means the − subtraction key on the right side of the keypad, not the (-) negative key near the bottom, which does nothing here. 2x² + 3x needs a plus, so press +, then enter to move along.
  3. Type the middle coefficient. Press 3, then enter. The highlight lands on the second sign.
  4. Make the last sign a minus. Press −, and the sign flips from + to −. Press enter to move to the last box.
  5. Type the constant. Press 2, then enter. The line now reads 2x² + 3x − 2 = 0, which is the equation you set out to solve.
    The TI-84 Evo Polynomial Root Finder showing 2x squared plus 3x minus 2 equals 0 fully entered
  6. Press SOLVE (the graph key again). Both roots arrive at once: x1 = −2 and x2 = ½, stacked as a real fraction rather than handed back as 0.5.
    The TI-84 Evo Polynomial Root Finder results screen showing x1 equals negative 2 and x2 equals one half as a stacked fraction

Cubics and higher

ORDER on the SETUP screen runs from 1 to 10, and nothing else about the app changes. Press SETUP (the window key), arrow along the ORDER row to 3, press enter, then NEXT. The coefficient screen grows a box for x³ and fills in the same way, one number and one sign at a time. Here is x³ − 6x² + 11x − 6 = 0 solved in one press:

The TI-84 Evo Polynomial Root Finder solving x cubed minus 6x squared plus 11x minus 6 equals 0, giving roots 1, 2 and 3

Good to know

  • Flip a root to a decimal. The last soft key on the results screen, the one marked with little arrows, sits on graph and switches the answers between exact and decimal form. The ½ becomes 0.5, and pressing it again brings the fraction back.
    The TI-84 Evo Polynomial Root Finder results with x2 shown as 0.5 instead of one half
  • Complex roots are one setting away. Left alone, the app answers x² + 1 = 0 with No real roots found. Press SETUP, arrow down to the row that starts with REAL, move right to a+bi and press enter. The same equation now comes back as x1 = −i and x2 = i.
    The TI-84 Evo Polynomial Root Finder solving x squared plus 1 equals 0 in a plus bi mode, giving negative i and i
  • Solve another one without starting over. COEFF (the zoom key) on the results screen goes back to the boxes with your numbers still in them, so you can change one coefficient and press SOLVE again. On that screen the same key is RESET, and its 1:Reset Defaults wipes everything back to 1x² + 0x + 0 = 0.
  • Send the polynomial to the graph. STORE (the trace key) on the results screen offers 2:Polynomial to Y=, which pastes the polynomial into the Y= list as Y1 and leaves it ready to draw. From there it graphs like anything else, covered in how to graph a function on the TI-84 Evo, and you can pin the same roots on the picture with the CALCULATE menu in how to find x- and y-intercepts on the TI-84 Evo.
  • Leaving the app. QUIT sits on the y= key and drops you back at the home screen. From there on flips between the home screen and the app grid, so it is also the way back in.
  • Which reset costs you the app. The everyday one is safe: MEMORY (2nd then the blue label above the toggle key) → 7:Reset → 1:All RAM only clears data and programs from RAM, and the p(x)=0 icon is still on the grid afterwards. It's the ALL tab's 1:All Memory that warns it deletes "all data, programs & Apps", and it means it: the root finder goes, along with Python and four other built-in apps.