ti 84 plus graphing calculator texas instruments

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Quadratic Equation Solver

Find roots for ax² + bx + c = 0

Calculation Results:

How to Use the Quadratic Solver

While the TI-84 Plus graphing calculator has a built-in Polynomial Root Finder app (PolySmlt), sometimes you need a quick solution without navigating through menus. This tool replicates the core functionality of solving for x in the standard form equation ax² + bx + c = 0.

Understanding the Discriminant

The key to solving these equations on the TI-84 or by hand is the discriminant (b² – 4ac). This value tells you what kind of roots to expect:

  • Positive Discriminant: There are two distinct real solutions where the graph crosses the x-axis.
  • Zero Discriminant: There is exactly one real solution (the vertex of the parabola touches the x-axis).
  • Negative Discriminant: The solutions are complex numbers involving imaginary parts (i), meaning the graph does not touch the x-axis.

Steps for TI-84 Plus Users

If you want to verify these results on your physical device, follow these steps:

  1. Press the [APPS] key.
  2. Scroll to PolySmlt and press [ENTER].
  3. Select 1: Polynomial Root Finder.
  4. Enter your degree (2 for quadratic) and the values for a, b, and c.
  5. Press [GRAPH] (F5) to see the solutions.

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