Quadratic Equation Solver Gaming Project in C++

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3 months ago

#include <iostream>
#include <cmath>
#include <complex>

// Function to solve the quadratic equation ax^2 + bx + c = 0
void solveQuadratic(double a, double b, double c) {
    if (a == 0) {
        std::cerr << "This is not a quadratic equation." << std::endl;
        return;
    }

    double discriminant = b * b - 4 * a * c;

    if (discriminant > 0) {
        // Two distinct real roots
        double root1 = (-b + std::sqrt(discriminant)) / (2 * a);
        double root2 = (-b - std::sqrt(discriminant)) / (2 * a);
        std::cout << "Roots are real and different:" << std::endl;
        std::cout << "Root 1 = " << root1 << std::endl;
        std::cout << "Root 2 = " << root2 << std::endl;
    } else if (discriminant == 0) {
        // One real root
        double root = -b / (2 * a);
        std::cout << "Roots are real and the same:" << std::endl;
        std::cout << "Root = " << root << std::endl;
    } else {
        // Complex roots
        std::complex<double> root1 = (-b + std::sqrt(std::complex<double>(discriminant))) / (2.0 * a);
        std::complex<double> root2 = (-b - std::sqrt(std::complex<double>(discriminant))) / (2.0 * a);
        std::cout << "Roots are complex and different:" << std::endl;
        std::cout << "Root 1 = " << root1 << std::endl;
        std::cout << "Root 2 = " << root2 << std::endl;
    }
}

int main() {
    double a, b, c;

    std::cout << "Enter coefficients a, b, and c: ";
    std::cin >> a >> b >> c;

    solveQuadratic(a, b, c);

    return 0;
}

#include <iostream>

#include <cmath>

#include <complex>

// Function to solve the quadratic equation ax^2 + bx + c = 0

void solveQuadratic(double a, double b, double c) {

if (a == 0) {

std::cerr << "This is not a quadratic equation." << std::endl;

return;

}

double discriminant = b * b - 4 * a * c;

if (discriminant > 0) {

// Two distinct real roots

double root1 = (-b + std::sqrt(discriminant)) / (2 * a);

double root2 = (-b - std::sqrt(discriminant)) / (2 * a);

std::cout << "Roots are real and different:" << std::endl;

std::cout << "Root 1 = " << root1 << std::endl;

std::cout << "Root 2 = " << root2 << std::endl;

} else if (discriminant == 0) {

// One real root

double root = -b / (2 * a);

std::cout << "Roots are real and the same:" << std::endl;

std::cout << "Root = " << root << std::endl;

} else {

// Complex roots

std::complex<double> root1 = (-b + std::sqrt(std::complex<double>(discriminant))) / (2.0 * a);

std::complex<double> root2 = (-b - std::sqrt(std::complex<double>(discriminant))) / (2.0 * a);

std::cout << "Roots are complex and different:" << std::endl;

std::cout << "Root 1 = " << root1 << std::endl;

std::cout << "Root 2 = " << root2 << std::endl;

}

int main() {

double a, b, c;

std::cout << "Enter coefficients a, b, and c: ";

std::cin >> a >> b >> c;

solveQuadratic(a, b, c);

return 0;

}

Explanation

Quadratic Equation:
- The general form of a quadratic equation is $ax^2 + bx + c = 0$ , where $a$ , $b$ , and $c$ are coefficients.
Discriminant:
- The discriminant of the quadratic equation is calculated as $discriminant=b2−4ac\text{discriminant} = b^2 – 4ac$ .
- The nature of the roots depends on the discriminant:
  - If the discriminant is positive, the equation has two distinct real roots.
  - If the discriminant is zero, the equation has one real root (a repeated root).
  - If the discriminant is negative, the equation has two complex roots.
Solving the Equation:
- Real Roots: When the discriminant is non-negative, the program calculates the roots using the quadratic formula:
- Complex Roots: When the discriminant is negative, the program uses the std::complex type to handle complex numbers.
User Input:
- The program prompts the user to enter the coefficients $a$ , $b$ , and $c$ , and then calls the solveQuadratic function to solve the equation and display the roots.

Explanation

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