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How to find all the roots of a polynomial on a TI-84 Plus CE, TI-84 Plus or TI-83 Plus

By E-Code · updated

Press APPS, pick PlySmlt2, any key, then 1 for the polynomial root finder; pick the ORDER and press GRAPH (NEXT). Type the coefficients with ENTER after each and press GRAPH (SOLVE): every root appears at once.

Step by step

  1. Open APPS. APPS Press APPS. It lists the apps on your calculator.
  2. Open PlySmlt2. 7 Press 7 for PlySmlt2, the polynomial root finder. On your own calculator its number may differ.
  3. Past the title. ENTER Press any key, here ENTER. The main menu opens.
  4. Polynomial root finder. 1 Press 1. The mode screen asks for the ORDER, the highest power of x. The cursor is on 2.
  5. Move to 3. ▶ Press ▶ once, onto 3: this is a cubic.
  6. Pick order 3. ENTER Press ENTER. 3 is now highlighted.
  7. Press NEXT. GRAPH Press GRAPH, the key under NEXT at the bottom of the screen. The keys under the screen work as its buttons.
  8. Type the coefficients. 1 ENTER (-) 6 ENTER 1 1 ENTER (-) 6 ENTER For x³ − 6x² + 11x − 6 = 0, type each number and ENTER: 1, (−)6, 11, (−)6.
  9. Solve. GRAPH Press GRAPH, now the key under SOLVE.
  10. Every root at once. x = 3, 2 and 1. With a+bi picked on the mode screen it finds complex roots too.

What the screen shows

x = 3, 2 and 1. With a+bi picked on the mode screen it finds complex roots too.

Look for x3=1 on the screen.

Try it with the keys lit up

This guide is one of E-Code's Learn lessons. Open it on E-Code's TI-84 calculator and each key lights up in turn as you press it.

Try “Find all the roots of a polynomial” on the TI-84 calculator

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