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Quadratic Roots

Quadratic Roots

Project Goals

This engineering effort invites you to combine what you learned about the basics of Python programming and mathematical functions to implement a useful program that can use an equation to find the roots for a quadratic equation. The program will have a command-line interface that accepts as input the values a, b, and c for a quadratic equation of the form \(f(x) = a \times x^2 + b \times x + c\). As you learn more about to translate mathematical equations into Python functions and you continue to enhance your technical skills, you will implement and test a complete Python program while using tools such as the VS Code text editor, a terminal window, and the Poetry package manager.

Project Access

If you are a student enrolled in a Computer Science class at Allegheny College, you can access this assignment by clicking the link provided to you in Discord. Once you click this link it will create a GitHub repository that you can clone to your computer by following the general-purpose instructions in the description of the technical skills. Specifically, you will need to use the git clone command to download the project from GitHub to your computer. Now you are ready to add source code and documentation to the project!


If you are an emerging proactive programmer who is not enrolled in a Computer Science class at Allegheny College, you can still work on this assignment! To get started, you should click the "Use this template" button in the quadratic-roots-starter GitHub repository and create your own version of this project's source code. After creating your GitHub repository, you can follow all of the other steps!

Expected Output

This project invites you to implement a quadratic root finding program called rootfinder. To learn more about the equations for finding the roots of a quadratic equation, please try out the quadratic formula calculator. For instance, input a=1, b=2, and c=1 into this calculator and see what answer it produces. After repairing your program, as explained in the next step of this assignment, it will also be possible for you to run the provided Python program by typing poetry run rootfinder --a 1 --b 2 --c 1 in your terminal window and observe that the programs produces the following output:

⭐ Calculating the roots of a quadratic equation with:
   a = 1.0
   b = 2.0
   c = 1.0

⭐ Finished computing the roots of the equation as:
   x_one = -1.0
   x_two = -1.0

Does the Python program produce the same output as the quadratic formula calculator site suggests it should? If it does, then try to run the program with different inputs by typing poetry run rootfinder --a 1 --b 1 --c 1. In this case, your program should produce the following output:

⭐ Calculating the roots of a quadratic equation with:
   a = 1.0
   b = 1.0
   c = 1.0

⭐ Finished computing the roots of the equation as:
   x_one = (-0.49999999999999994+0.8660254037844386j)
   x_two = (-0.5-0.8660254037844386j)

Is this output the same as what the web-based quadratic formula calculator produces? Please note that the output of this program includes numbers like -0.5-0.8660254037844386j, which means that this is a program that has an "imaginary" component. If you would like to learn more about "imaginary" numbers and how you can intuitively and geometrically interpret them, please read the visual and intuitive guide to imaginary numbers, bearing in mind that the referenced article uses the variable i and Python programs always use the variable j to mean the same thing. Finally, please make sure that you try your program with several additional inputs, always confirming that it works correctly by using the web-based quadratic formula calculator.


Remember, if you want to run rootfinder you must use your terminal to go into the GitHub repository containing this project and then go into the rootfinder directory that contains the project's source code. Finally, remember that before running the program you must run poetry install to add the dependencies. If you run into errors when using a poetry run command you can often resolve them by deleting the .venv directry and the poetry.lock file and then trying poetry install again.

Adding Functionality

If you study the file rootfinder/rootfinder/ you will see that it has many TODO markers that designate the parts of the program that you need to implement before rootfinder will produce correct output. If you run the provided test suite with the command poetry run task test you will see that it produces output like the following:

================================= FAILURES =================================
__________________ test_calculate_x_values_non_imaginary ___________________

    def test_calculate_x_values_non_imaginary():
        """Check that the calculation of x values works if they are not imaginary."""
        a = 1
        b = 2
        c = 1
>       x_one, x_two = rootfind.calculate_quadratic_equation_roots(a, b, c)
E       TypeError: cannot unpack non-iterable NoneType object

tests/ TypeError

Alternatively, running the program with a command like poetry run rootfinder --a 1 --b 2 --c 1 will not produce any output! This is due to the fact that the required source code does not yet exist inside of the rootfinder program. One function that you need to implement is specified by the following signature.

def calculate_quadratic_equation_roots(
    a: float, b: float, c: float
) -> Tuple[Union[float, complex], Union[float, complex]]:

This function's type annotations on line 2 suggest that each of its three inputs are variables of type float. On line 3, the notation Union[float, complex] means that one of the outputs of calculate_quadratic_equation_roots can either be a floating-point value of type float or an imaginary number of type complex. The complete annotation of Tuple[Union[float, complex], Union[float, complex]] means that the return value of calculate_quadratic_equation_roots will be a two-tuple of values, with each component of the two-tuple being either a float or a complex number. This function should return values for x_one and x_two according to the following equations:

\[ x_1=\frac{-b+\sqrt{b^2-4ac}}{2a} \]
\[ x_2=\frac{-b-\sqrt{b^2-4ac}}{2a} \]

To provide a command-line interface to your program, you should also implement a main function that has the following signature:

def main(
    a: float = typer.Option(1),
    b: float = typer.Option(2),
    c: float = typer.Option(2)

This function signature shows that rootfinder accepts as input three parameters called a, b, and c that respectively have default values of 1, 2, and 2, as seen on lines 2 through 4. If you run poetry run rootfinder if should produce this output:

⭐ Calculating the roots of a quadratic equation with:
   a = 1.0
   b = 2.0
   c = 2.0

⭐ Finished computing the roots of the equation as:
   x_one = (-0.9999999999999999+1j)
   x_two = (-1-1j)

Running Checks

If you study the source code in the pyproject.toml file you will see that it includes the following section that specifies different executable tasks like lint. If you are in the square directory that contains the pyproject.toml file and the poetry.lock file, the tasks in this section make it easy to run commands like poetry run task lint to automatically run all of the linters designed to check the Python source code in your program and its test suite. You can also use the command poetry run task black to confirm that your source code adheres to the industry-standard format defined by the black tool. If it does not adhere to the standard then you can run the command poetry run black square tests and it will automatically reformat the source code.

Along with running tasks like poetry run task lint, you can leverage the relevant instructions in the technical skills to run the command gatorgrade --config config/gatorgrade.yml to check your work. If your work meets the baseline requirements and adheres to the best practices that proactive programmers adopt you will see that all the checks pass when you run gatorgrade. You can study the config/gatorgrade.yml file in your repository to learn how the GatorGrade program runs GatorGrader to automatically check your program and technical writing. If your program has all of the anticipated functionality, you can run the command poetry run task test and see that the test suite produces output like the following. Notice that the current test suite only has three test cases! If you are looking for an additional challenge, consider using the quadratic formula calculator to guide you as you create new test cases for calculate_quadratic_equation_roots that run in Pytest.

collected 3 items

tests/ ...

Don't forget that when you commit source code or technical writing to your GitHub repository for this project, it will trigger the run of a GitHub Actions workflow. If you are a student at Allegheny College, then running this workflow consumes build minutes for the course's organization! As such, you should only commit to your repository once you have made substantive changes to your project and you are ready to confirm its correctness. Before you commit to your repository, you can still run checks on your own computer by either using Poetry or Docker and GatorGrader.

Project Reflection

Once you have finished both of the previous technical tasks, you can use a text editor to answer all of the questions in the writing/ file. For instance, you should provide the output of the Python program in a fenced code block, explain the meaning of the Python source code segments that you implemented and used, and answer all of the other questions about your experiences in completing this project. For instance, your technical writing in the writing/ file should make it clear that you understand the concept of an "imaginary" number and the notation that the Python programming language uses to express these numbers.


To ensure that you master the technical and professional skills introduced as part of this project you need to participate in deliberate practice that "requires both a clear performance goal and immediate informative feedback".1 After reflecting on the challenges that you faced and identifying areas for improvement, make a list of SMART goals that will enable you to more effectively put a specific technical skill into practice, follow your plan, and continually work to improve.2 You can learn more about how to best reflect on your experiences and improve before starting your next project by reviewing the technical skills that a proactive programmer should master!

Project Assessment

Since this project is an engineering effort, it is aligned with the evaluating and creating levels of Bloom's taxonomy. You can learn more about how a proactive programming expert will assess your work by examining the assessment strategy. From the start to the end of this project you may make an unlimited number of reattempts at submitting source code and technical writing that meet every aspect of the project's specification.


Before you finish all of the required deliverables required by this project is worth pausing to remember that the instructor will give advance feedback to any learner who requests it through GitHub and Discord at least 24 hours before the project's due date! Seriously, did you catch that? This policy means that you can have a thorough understanding of ways to improve your project before its final assessment! To learn more about this opportunity, please read the assessment strategy for this site.

Seeking Assistance

Emerging proactive programmers who have questions about this project are invited to ask them in either the GitHub discussions forum or the Proactive Programmers Discord server. Before you ask your question, please read the advice concerning how to best participate in the Proactive Programmers community. If you find a mistake in this project, please describe it and propose a solution by creating an issue in the GitHub Issue Tracker.

  1. See Merriam-Webster for the definition of Teaching Tech Together for more details about how to effectively learn technical skills. What practical steps can you take to best ensure that you can master the technical skills of a proactive programmer? 

  2. See the article called How to write SMART goals for an overview of how to create SMART goals that are specific, measurable, achievable, relevant, and time-bound. In your view, what are the benefits of ensuring that your goals fit into the SMART paradigm? 

Updated: 2023-03-17   Created: 2021-08-12
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