When I execute the problem, the results often end up as "-nan' or "nan" I am new to programming so this is a bit confusing. Could use some help

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


//Quadratic Equation
int main() {

 //Variables
 double a,b,c,n,z,x1,x2,r;    

 //Input
 cout<<"Quadartic Equation Calculator"<<endl<<endl;     
 cout<<"What is you 'a' value?: "<<endl;
 cin>>a;
 cout<<"What is your 'b' value?:  "<<endl;
 cin>>b;
 cout<<"What is your 'c' value?:  "<<endl;  
 cin>>c;  

 //calculation
  n = -b;
  z = sqrt((b*b)-(4*a*c));
  r= 2*a;
  x1 = (n (z))/r;
  x2 = (n-(z))/r;

//output
 cout<<"Your Solutions are:  "<< x1 << " or "<< x2;

 return 0;             
 }

`

CodePudding user response：

std::sqrt() in the <cmath> header expects its argument to be a positive number, in case it isn't, it will return nan which is what you are facing. It also raises the FE_INVALID floating point exception which you can verify after calling the std::sqrt() function using std::fetestexcept(FE_INVALID).

In actual math, square roots of negative numbers result in complex numbers. Ordinary floating-point types like double which usually follow the IEEE-754 standard are not capable of representing complex numbers. For that, you need to use something like std::complex<double> which is actually capable of storing complex numbers inside it.

Below is your code modified to utilize std::complex<double> and will properly print the real and imaginary part separately for square roots of negative real numbers instead of simply returning nan as it did before.

#include <iostream>
#include <complex>

using namespace std;

double abs_zero(double const x) {
    return x == 0 ? 0 : x;
}

int main() {
    // Variables
    complex<double> a, b, c, n, z, x1, x2, r;

    // Input
    cout << "Quadartic Equation Calculator" << endl << endl;
    cout << "What is your 'a' value?: " << endl;
    cin >> a;
    cout << "What is your 'b' value?: " << endl;
    cin >> b;
    cout << "What is your 'c' value?: " << endl;
    cin >> c;

    // Calculation
    n = -b;
    z = sqrt((b * b) - (complex<double>(4, 0) * a * c));
    r = complex<double>(2, 0) * a;
    x1 = (n   z) / r;
    x2 = (n - z) / r;

    x1 = complex<double>(abs_zero(real(x1)), abs_zero(imag(x1)));
    x2 = complex<double>(abs_zero(real(x2)), abs_zero(imag(x2)));

    // Output
    if (imag(x1) == 0)
        cout << "Your Solutions are: " << real(x1) << " or "<< real(x2) << endl;
    else
        cout << "Your Solutions are: " << x1 << " or " << x2 << endl;
}

In case you'd like to try it out yourself, here you are:

Demo

CodePudding user response：

"Often" end up as nan or -nan? That's expected behaviour. The quadratic formula gives you the roots of the equation, where the graph intersects the x-axis. Not all quadratic equations intersect the x-axis.

When you input a quadratic that doesn't intersect the x-axis into the quadratic formula, you end up with a negative number in the square-root of the equation, which leads to an imaginary number, which cannot be represented by the float/double data type, and thus you get "nan" or "-nan".

CodePudding user response：

NAN is in short for "Not a Number" is an exception which usually occurs in the cases when a number can’t be represented. Its probably that sqrt((bxb)-(4ac)) is causing the error as for some inputs the square root of that input would be undefined. For example in case of a = 5, b = 4 and c = 3, sqrt((bxb)-(4ac)) is undefined as it is sqrt. of negative number.