Quadratic Root Solving

Background

$$x = \frac{-b \pm \sqrt{ b^2 - 4 a c}}{2a} \ $$

Figure 1: This expression is the quadratic formula.

$$ax^2 + bx + c$$

Figure 2: This is the quadratic equation of a parabola. The formula in Figure1 will find the cooridinates where the parabola crosses the X axis

$$ \ $$

Figure 3: The equation of this parabola is $f(x) = x^2 - 4$, its roots are -2 and 2 because those are the x cooridinates at which the parabola crosses the X axis.

Rules For Real Roots

1. If the discriminant in Figure 1 ($b^2 - 4 a c$) is greater than zero, then there will be two real roots
2. If the discriminant is zero, then there will be one real root
3. If the discriminant is less than zero, there will be no real roots

Two Roots Example

See Figure 3

One Root Example

Figure 4: $f(x) = x^2$, there exists one root because the discriminant in Figure 1 of $(0^2) - 4(1)(0)$ is equal to 0, where a is 1, b is 0, and c is 0.

No Root Example

Figure 5: $f(x) = x^2 + 4$, there exists one root because the discriminant in Figure 1 of $(0^2) - 4(1)(4)$ is less than 0, where a is 1, b is 0, and c is 4.

Usage

Option #1

1. Compile C++ file and execute the executable from the terminal

g++ quadratic_formula.cpp -o a.out && ./a.out

2. Insert the coefficients of the formula

a: <1>
b: <0>
c: <0>

3. View the output

root 1: 0

Option #2

1. Compile C++ file and execute the executable from the terminal with the coefficients as arguments

g++ quadratic_formula.cpp -o a.out && ./a.out 1 0 0

2. View the output

root 1: 0

Shell Script Unit Testing

The repository contains a file called test_suite.sh which contains a shell script that tests the quadratic root solver, currently test_suite.sh has the test cases hard coded within the file, it would be better for the script to read the test cases from a text file, that way the user coulld easily add their own test cases

./test_suite.sh 

Make sure that before any commits are pushed to the repository, that all test cases passed.

TEST-CASE #1 PASSED 
TEST-CASE #2 PASSED