Table of Contents

Quadratic Equation Software Manual

This is a template file for building an entry in the student software manual project. You should use the formatting below to define an entry in your software manual.

Routine Name: quadratic_equation

Author: Philip Nelson

Language: C++. The code can be compiled using the GNU C++ compiler (gcc). A make file is included to compile an example program

For example,

make

will produce an executable ./quadratic.out that can be executed.

Description/Purpose: This routine computes the solutions to the second order polynomial, \(ax^2 + bx + c\) and returns both solutions if they exist.

Input: There are three inputs required which represent \(a,b,c\) of the second order polynomial.

Output: This routine returns an optional array of two numbers matching the type of the input parameters. If the solutions are real, they are returned in an optional array. If the solutions are imaginary, the optional is returned with no values. Thus, the caller must check if the result has any value.

Usage/Example:

#include "quadraticEquation.hpp"
#include <iostream>

int main()
{
  auto res = quadratic_equation(2.0, 9.0, -5.0);
  if (res)
  {
    auto [r1, r2] = res.value();
    std::cout << "( " << r1 << " , " << r2 << " )\n";
  }
  else
  {
    std::cout << "imaginary roots\n";
  }

  res = quadratic_equation(2.0, 3.0, 5.0);
  if (res)
  {
    auto [r1, r2] = res.value();
    std::cout << r1 << ' ' << r2 << '\n';
  }
  else
  {
    std::cout << "imaginary roots\n";
  }
  return EXIT_SUCCESS;
}

Output from the lines above

( 0.5,-5 )
imaginary roots

The first line contains the roots from the equation \(2x^2 + 9x - 5\). The second equation \(2x^2 + 3x + 5\) has imaginary roots as is reported in the second line.

Implementation/Code: The following is the code for quadratic_equation

#include <array>
#include <cmath>
#include <optional>

template <typename T>
std::optional<std::array<T, 2>> quadratic_equation(T a, T b, T c)
{
  const auto descrim = (b * b) - (4.0 * a * c);
  if (descrim > 0)
  {
    const T r1 = (-b + sqrt(descrim)) / (2.0 * a);
    const T r2 = (-b - sqrt(descrim)) / (2.0 * a);

    return std::array {r1, r2};
  }
  return {};
}

Last Modified: September 2018