Question

a. Write a C++ program to determine the root of a number.
b. Modify the program in 3(a) above to determine the real, equal and imaginary roots of a
quadratic equation.
c. Draw the flowchart of 3(b)

Answer 1

#include <iostream> // to use cin/cout
#include <math.h> // for function "sqrt"
using namespace std;
double getroot(double X)
{
    // next line finds root of number by standart function in c++
    // if you can use standart functions, just uncomment next line ans delete other code in function
    // return sqrt(X); // uses standart library "math.h"
    // finding root using binsearch
    double l = 0, r = X, mid;
    while (r - l > 0.0000001)
    {
        mid = (l + r) / 2.0;
        if (mid * mid < X)
            l = mid;
        else
            r = mid;
    }
    return l;
}
int main()
{
    double X;
    do
    {
        // write information for user
        cout << "Enter the number(for end of program enter negative number): ";
        // read number
        cin >> X;
        // call our function
        if(X >= 0)
            cout << "Root of a number is: " << getroot(X) << "\n";
    }
    while(X >= 0);
    return 0;
}
#include <iostream> // to use cin/cout
#include <math.h> // for function "sqrt"
using namespace std;
double getroot(double X)
{
    // next line finds root of number by standart function in c++
    // if you can use standart functions, just uncomment next line ans delete other code in function
    // return sqrt(X); // uses standart library "math.h"
    //finding root using binsearch
    double l = 0, r = X, mid;
    while (r - l > 0.0000001)
    {
        mid = (l + r) / 2.0;
        if (mid * mid < X)
            l = mid;
        else
            r = mid;
    }
    return l;
}
int main()
{
    cout << "A*x^2 + B*x + C = 0\n\n";
    double A, B, C, D, x1, x2, im_x1, im_x2;
    do
    {
        // write information for user
        cout << "\nEnter coefficients A, B, C (for end of program enter coefficient A equals to zero): \n";
        // read coefficients
        cin >> A >> B >> C;
        // let D = B*B - 4*A*C
        // we know that roots x1, x2 = (-B +/- sqrt(D)) / (2*A)
        // so, if D < 0 - there are imaginary roots
        // if D == 0 - we have one real root
        // and if D > 0 - we have two real roots
        if (A != 0)
        {
            D = B*B - 4.0*A*C;
            cout.precision(2);
            if (D < 0)
            {
                // imaginary roots
                cout << "There are imaginary roots\n";
                x1 = -B/(2*A);     //real part of first root
                im_x1 = -getroot(-D) / (2*A); // imaginary part of first root
                x2 = -B/(2*A);     //real part of second root
                im_x2 = getroot(-D) / (2*A); // imaginary part of second root
                cout << x1 << " + i*(" << im_x1 << ")\n";
                cout << x2 << " + i*(" << im_x2 << ")\n";
            }
            else if(D == 0)
            {
                // one real root
                cout << "There is one real root\n";
                x1 = B / (-2.0*A);
                cout << fixed << x1 << "\n";
            }
            else
            {
                // two real roots
                cout << "There are two real roots\n";
                x1 = (-B - getroot(D)) / (2.0*A);
                x2 = (-B + getroot(D)) / (2.0*A);
                cout << fixed << x1 << " " << x2 << "\n";
            }
        }
    }
    while(A != 0);
    return 0;
}