DiscriminantTI

A program to calculate the Discriminant of a quadratic polynomial and the corresponding zeros for the Texas Instruments TI-84 Plus.

Disclaimer: I wrote this basic program back when I was 16. The code has not been changed ever since, however, I decided to release it now. :)

Mathematics Refresher

Quadratic function

The quadratic function is one of the form f(x) = ax² + bx + c. In the formula, x refers to an unknown variable; a, b, and c refer to the coefficients representing known real or complex numbers. However, coefficient a can not be 0. To solve the equation, the unknown variable x is also referred to as roots or zeros, can be solved as follows:

Whereas the plus-minus symbol should be solved separately, resulting in two roots.



Under the root, the quantity Δ = b² - 4ac is known as the discriminant of the quadratic equation.

Discriminant

The discriminant in this case refers to a polynomial function of the coefficients of the original polynomial. As referred to above, the program will cover the quadratic polynomial ax² + bx + c = 0, whereas the discriminant of the quadratic polynomial is b² - 4ac.

Assumptions

If a ≠ 0; the discriminant is zero if and only if the polynomial has a double root.
If real coefficients; the discriminant is positive if the polynomial has two disctinct real roots.
If real coefficients; the discriminant is negative if the polynomial has two disctinct complex conjugate roots.

Using the program

Info

This program was coded to enhance the efficiency of solving the discriminant and finding the zeros during my classes of mathematics. It's developed to use on the Texas Instruments TI-84 Plus calculators.

The program captures the quadratic formula by user input of a, b, and c.

Mathematics behind the program

As an example, in function f(x) = 4x² - 6x + 2, we understand that a = 4, b = -6, and c = 2.

Solving the Discriminant goes as follows:
f(x) = 4x² - 6x + 2
x = (-6)² - 4.4.2
x = 36 - 32
x = 4

X is positive in this case, meaning there are two real roots.

x = [-b ± √(b2 - 4ac)]/2a
x = [-(-6) ± √((-6)² - 4.4.2)]/2.4
x = [6 ± √4]/8
x = (6 - 2)/8 and (6 + 2)/8
x = 0.5 and x = 1

In the quadratic function f(x) = 4x² - 6x + 2 the parabola will have zeros at x = 0.5 and x = 1.

The program solves all 3 formulas in less than 1 second. :)

Setup

Requirements

TI Connect CE software. Link: https://education.ti.com/en/products/computer-software/ti-connect-ce-sw

Latest version of DiscriminantTI application

TI-84 Plus calculator with cable

Installation

1. Install the TI Connect software and driver.
2. Connect the TI-84 Plus calculator to your computer using the cable.
3. Download the DiscriminantTI application from GitHub.
4. Open the TI Connect software and head over to the 3rd vertical tab. (3 square blocks)
5. Click on "Open Program" and select the DiscriminantTI application.
6. Click on "Actions" (4th horizontal tab) and click on "send to calculators".

The application is now available on the calculator by using the "PRGM" button. (3rd row, 3rd button)

Troubleshooting

The application may throw an error after you have entered the 3 variables:

Your discriminant is negative; hence, the parabola will not have any zeros on the x-axis.

In this case, you will be greeted with the "ERR: NONREAL ANS" error. Click on "Quit" or option "1". The program will show you the negative discriminant.

You have used the "-" button instead of the "(-)" button. Kindly note that you have to enter negative values using the (-) button.

You have entered the wrong '-' sign; you will be greeted immediately with "ERR: SYNTAX". Click on "Goto" or option "2" and replace the "-" sign with "(-)".

Further development

I have no plans to further develop more functionality.
However, this leaves room for you to develop further upon the basics. :)