# | include: false
import numpy as np
import pandas as pd
np.random.seed(256852)Using Jupyter (Need), Exercises
Exercise 1 (Put it in Markdown) ☻
1 Quadratic Equations
Introduction
(Image from the Wikipedia page on Quadratic equations)
The general form of a quadratic equation is:
\[ ax^2 + bx + c = 0 \]
Solutions
Provided \(a\ne0\), we can use an elementary algebraic method called completing the square to show that a quadratic equation has the following solution: \[ x = {-b \pm \sqrt{b^2-4ac} \over 2a} \]
Discriminant
The quantity \(\Delta = b^2-4ac\) is called the discriminant of the equation and decides the nature of its solutions. The table below shows the various possibilities.
| Discriminant | Roots |
|---|---|
| \(\Delta = b^2-4ac = 0\) | A single solution of \(-b/(2a)\) |
| \(\Delta = b^2-4ac \gt 0\) | Two distinct solutions |
| \(\Delta = b^2-4ac \lt 0\) | No real solutions; both are complex. |
Use a Markdown cell to reproduce the short introduction to quadratic equations presented in the Result tab.
Exercise 2 (In your own words) ☻
Use a Markdown cell to answer the following.
- What is a Git repository?
- Git keeps tracks of ____BLANK____ in the files in our repository.
- What is a commit?
- What is a push?
- What is a pull?
- What is the difference between GitHub and GitHub Desktop?