Algorithm:

1. Create a class roots with coefficients a, b and c and roots r1 and r2 as data members and getdata(), determinant() and checkdeterminant() as member functions.
2. getdata() takes input from user and initialize the data members a, b, c and define determinant() so that it can compute (b*b)-(4*a*c). If the determinant is 0 then the roots must be equal so assign them the value –b/2a and print the result. If the determinant is positive then roots must be distinct and real so calculate two roots -b+sqrt(d)/2a and -b-sqrt(d)/2a and print the result. If the determinant is negative then roots must be imaginary so calculate real and virtual part –b/2a and sqrt(-d)/2a and print result.
3. Create an object r of class roots.
4. Input the coefficients using the getdata().
5. Compute determinant using determinant().
6. Check determinant and print the roots using checkdeterminant().

C++ code to find the roots of quadratic equation

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

//class
class roots {
	int a, b, c;
	float r1, r2;
	public:
		void getdata();
		int determinant();
		void checkdeterminant(int);
};

void roots::getdata() {
	cout << "Enter value of coefficient of x^2: ";
	cin >> a;
	cout << "Enter value of coefficient of x: ";
	cin >> b;
	cout << "Enter value of coefficient of 1: ";
	cin >> c;
}

int roots::determinant() {
	int d = b * b;
	d -= (4 * a * c);
	return d;
}

void roots::checkdeterminant(int d) {
	if (d == 0) {
		cout << "Real and equal roots\n";
		r1 = (-1 * b);
		r1 /= (2 * a);
		r2 = r1;
		cout << "Roots : " << r1 << " and " << r2 << endl;
	}
	else if (d > 0) {
		cout << "Real and distinct roots\n";
		r1 = (-1 * b) + sqrt(d);
		r1 /= (2 * a);
		r2 = (-1 * b) - sqrt(d);
		r2 /= (2 * a);
		cout << "Roots : " << r1 << " and " << r2 << endl;
	}
	else {
		cout << "Imaginary roots" << endl << endl;
		r1 = (-b)/(2*a);
		r2 = (sqrt(-d))/(2*a);
		cout << "Roots : " << r1 << " + i" << r2 ;
		cout << " and " << r1 << " - i" << r2 << endl<<endl;
	}
}

int main() {
	roots r;
	
	r.getdata();
	
	cout << endl;
	int d = r.determinant();
	r.checkdeterminant(d);
	cout << endl;
	
	return 0;
}

Output

First run:
Enter value of coefficient of x^2: 1
Enter value of coefficient of x: 4
Enter value of coefficient of 1: 4

Real and equal roots
Roots : -2 and -2

Second run:
Enter value of coefficient of x^2: 1
Enter value of coefficient of x: -5
Enter value of coefficient of 1: 6

Real and distinct roots
Roots : 3 and 2

Third run:
Enter value of coefficient of x^2: 1
Enter value of coefficient of x: 3
Enter value of coefficient of 1: 4

Imaginary roots
Roots : -1 + i1.65831 and -1 - i1.65831