C++ Program to find roots of a quadratic equation

Here we are discussing a C++ program to find all roots of a quadratic equation.

What is a quadratic equation?

In math, we define a quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is y = ax² + bx + c, where a, b, and c are numbering and a cannot be 0. 

Example : 6x² + 11x – 35 = 0.

How to find the roots of a quadratic equation?

For a quadratic equation ax² + bx + c = 0, The roots are calculated using the formula,

x = (-b ± √ (b² - 4ac) ) / 2a    

Where,

• a, b, and c are coefficients.
• b² - 4ac is called the discriminant.

With respect to the value of discriminant the roots of the equation will be

• If the discriminant of the equation is greater than zero, then the roots will be real and different
• If the discriminant of the quadratic is Zero, then the roots will be real and equal.
• If the discriminant of the equation is less than zero, then the roots are complex and different.

How to calculate the roots of a quadratic equation using C++ program?

Ask the user to enter the value of three variables a, b, and c. First, calculate the value of the discriminant by using the formula, Discriminant = b² - 4ac. Store the value to variable discrim, which is of float type.

For the discriminant value, we have three conditions. as we discussed above which will be less than or equal to, or greater than zero. This can be done by using the if….else if….else statement.

If the value of discrim is greater than zero ( discrim > 0 ) calculate the roots by the formula  (-b ± √ (b² - 4ac) )/2a. In this equation, the square root will find out using the function sqrt function. The sqrt() function in C++ is used for calculating the square root. it is defined in the cmath header of C++.

• R1=  (-b + √ (b² - 4ac) )/2a and 
• R2 =  (-b - √ (b² - 4ac) )/2a
• Print R1 and R2.

Else if the discriminant value is equal to zero ( discrim = = 0 )

• Root R1 = root R 2 
• R1 = -b / 2a
• Print R1

Else there are two parts real part and the imaginary part.

• The real part is calculated by using the formula rpart = -b / 2a;
• Imaginary part is calculated by using the formula ipart  =  i√- (b² - 4ac) )/2a
• Print the imaginary part and the real part.

Algorithm

Step 1:  Call the header file iostream.

Step 2: Call the header file cmath.

Step 3: Use the namespace std

Step 4: Open the main function int main().

Step 5: Declare float variables; a, b, c, R1, R2, discrim, ipart,  rpart

Step 6: Print a message to enter coefficients a, b, and c;

Step 7: Read the numbers into the variables a, b, and c.

Step 8: Calculate the discriminant discrim =  b2 - 4ac.

Step 9: if the discrim >0

• Then R1=  (-b + sqrt(discrim )/2a and 
• R2 =  (-b - sqrt(discrim )/2a
•  Print R1 and R2

      Else if discrim = 0

• Then R1 = R2
• R1 = -b / 2a

      Else if discrim < 0

• Real part rpart = -b / 2a;
• Imaginary part ipart = i√- sqrt(discrim)/2a
• Print rpart and ipart

Step 10: Exit

                                          #include <iostream>
#include <cmath>
using namespace std;

int main() {

    float a, b, c, R1, R2, discrim, rPart, iPart;
    cout << "Enter coefficients a, b and c: ";
    cin >> a >> b >> c;
    discrim= b*b - 4*a*c;
    
    if (discrim> 0) {
        R1 = (-b + sqrt(discrim)) / (2*a);
        R2 = (-b - sqrt(discrim)) / (2*a);
        cout << "Roots are real and different." << endl;
        cout << "R1 = " << R1 << endl;
        cout << "R2 = " << R2 << endl;
    }
    
    else if (discrim == 0) {
        cout << "Roots are real and same." << endl;
        R1 = -b/(2*a);
        cout << "R1 = R2 =" << R1 << endl;
    }

    else {
        rPart = -b/(2*a);
        iPart =sqrt(-discrim)/(2*a);
        cout << "Roots are complex and different."  << endl;
        cout << "x1 = " << rPart << "+" << iPart << "i" << endl;
        cout << "x2 = " << rPart << "-" << iPart << "i" << endl;
    }

    return 0;
}
                                      

Enter coefficients a, b and c: 5
3
6
Roots are complex and different.
x1 = -0.3+1.05357i
x2 = -0.3-1.05357i