Roots in Quadratic Equations
Yaser Rahmati | یاسر رحمتی
A second-order equation, also known as a quadratic equation, is typically written in the form:
To find the roots of such an equation, you can use the quadratic formula:
Here's a step-by-step guide on how to use the quadratic formula:
Identify the coefficients:
In the equation , , , and are the coefficients. , , and can be any real numbers, including zero.
Plug the coefficients into the quadratic formula:
Once you have identified the coefficients , , and , plug them into the quadratic formula:
Calculate the discriminant:
The discriminant, , is part of the quadratic formula. It determines the nature of the roots. There are three cases:
If , the quadratic equation has two distinct real roots.
If , the quadratic equation has one real root (a repeated root).
If , the quadratic equation has two complex roots.
Example
Let's say we have the equation .
Identify the coefficients: , , and .
Plug the coefficients into the quadratic formula:
So, the roots are:
Python Code
This code defines a function find_roots
that takes the coefficients a
, b
, and c
of the quadratic equation as input and returns the roots.
Depending on the value of the discriminant, it calculates real roots, repeated roots, or complex roots accordingly.
You can replace the values of a
, b
, and c
with your own coefficients to find the roots of any specific quadratic equation.
My Training Video
Keywords
Web Development (Django, Flask)
, Data Science (Pandas, NumPy, Matplotlib)
, Machine Learning (Scikit-learn, TensorFlow, PyTorch)
, Artificial Intelligence
, Automation
, GUI Development (Tkinter, PyQt)
, Game Development (Pygame)
, Scientific Computing
, Financial Analysis (Pandas, NumPy
) , Network Programming
, Image Processing (OpenCV)
, Web Scraping (Beautiful Soup, Scrapy)
, Internet of Things (IoT) Development
, Robotics
, Cybersecurity
, Mobile App Development (Kivy)
, Cloud Computing (Boto3, AWS Lambda)
, Big Data Analysis (PySpark)
, Geographical Information Systems
, Natural Language Processing (NLTK, spaCy)
, Data Visualization (Seaborn, Plotly)
, Bioinformatics (Biopython)
, Multimedia Applications
, Education and Teaching
Last updated