Quadratic Formula how to get imaginary numbers

[Sasquadge]

Hey guys I'm new to programing and I made a program to solve quadratic formula but it doesn't work with imaginary numbers when the number is negative I get something like this -1.#IND. What can I add or adjust in my code to help get the program to show imaginary 'complex numbers'. Thanks!

Edit: Also is there a way to do this without the #include <complex>\

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

double a, b, c, rootvalue1, rootvalue2;

int main()
{

    cout <<"This program will have you enter coefficients a,b, and c.\n"                  //Explains what the program will do.
        "This will calculate two root values using the quadratic formula." << endl;
    cout <<"Enter Coefficient a: ";
    cin >> a;

    if (a == 0)                                                                             //If user enters 0 it will quit the program and give them error message.
    {
        cout << "0 is not a sufficient coefficient for this program.\n";
        cout <<"Restart now and try again." << endl;
        exit(0);
    }

    cout <<"Enter Coefficient b: ";
    cin >> b;
    cout <<"Enter Coefficient c: ";
    cin >> c;

    rootvalue1 = (-b + sqrt(b * b - 4 * a * c)) / (2 * a);         // Quadratic formula
    rootvalue2 = (-b - sqrt(b * b - 4 * a * c)) / (2 * a);          


    cout <<"The first Root Value = " << rootvalue1  << endl;          //Roo Answer
    cout <<"The second Root Value = " << rootvalue2  << endl;

    return 0;
}

[mike_2000_17]

If you want to compute complex numbers, then you should use the <complex> header and use the std::complex<double> type to represent your numbers. However, if you want to avoid it (why?), then you can simply check the value inside the square-root to see if it is negative (thus, leading to an imaginary component if the square root is taken). The sqrt function (when applied to double variables) will produce a NaN if the number is negative (btw, NaN means "Not a Number").

So, simply compute the square-rooted part separately, check it for negativity, and if it is negative than calculate the real and imaginary parts separately. If positive, then just use the code you have now.

[Sasquadge]

This is why not the complex include these were the instruction I was given but doesn't quite make sense to me. I got it to work with the complex include but I don't think that's what is wanted.

1. The quadratic formula fails if coefficient ais 0. If the user enters a 0 for a, print an appropriate error message and end the program (skip all calculations, do not loop).
   You may use exit(0);if you want. If you do, #include <stdlib.h>

2. The discriminant, b^2 - 4ac, describes the roots of a quadratic equation: if it is greater than or equal to 0, there are two real roots; and if it is less than 0, there are two complex roots.

a. Complex numbers are displayed with a real part and an imaginary part: e.g., 6 +
3iand 6 - 3i

b. The real part (6 in the example) is calculated by the formula -b/2a

c. The imaginary part (3i in the example) is calculated by the formula
sqrt(descriminant)/2a with an ‘i’ character printed at the end

d. Taking the square root of a negative number with the sqrt function causes a
runtime error, so the discriminant must be negated (i.e., multiplied by -1) before
taking the square root

1. Your program should find the roots in all three situations (the lab 1 version should work when the discriminant = 0 or > 0); your modifications for lab 2 should handle the case when the discriminant is < 0.

2. Follow the link in the lab 2 notes to see some formulas and discussion that might be
   useful.

[mike_2000_17]

Those instructions are pretty detailed. Do you have any specific problem in implementing them? You cannot just say "how do I do it" and expect complete code for it.

[Sasquadge]

well I don't want the whole code I'm trying to figure out I guess maybe somewhere to start would help I tried putting in those equation into the program but don't seem to get the results I'm looking for. Our practice test is
a=2
b=2
c=2
x1= -0.5 + 0.866025i
x2= -0.5 - 0.866025i

and -0.5 is supposed to be the real and I'm getting -2 and nothing near the 0.866025

[mike_2000_17]

As said in your instructions, the real part is calculated as:

double real_part = -b / (2.0 * a);

So, you say you calculated that value, from a = 2, b = 2, and c = 2, and got -2? How can -2 / (2 * 2) == -2? You must have inputted the formula wrong. What code do you have so far?

[Sasquadge]

This is what I got.

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

double a, b, c, rootvalue1, rootvalue2, real, descriminant, complex;

int main()
{

    cout <<"This program will have you enter coefficients a,b, and c.\n"                  
        "This will calculate two root values using the quadratic formula." << endl;
    cout <<"Enter Coefficient a: ";
    cin >> a;
    if (a == 0)                                                                             
    {
        cout << "0 is not a sufficient coefficient for this program.\n";
        cout <<"Restart now and try again." << endl;
        exit(0);
    }

    cout <<"Enter Coefficient b: ";
    cin >> b;
    cout <<"Enter Coefficient c: ";
    cin >> c;

    descriminant = pow(b,2) - (4 * a * c);
    rootvalue1 = (-b + sqrt(b * b - 4 * a * c)) / (2 * a);         
    rootvalue2 = (-b - sqrt(b * b - 4 * a * c)) / (2 * a);  
    real = -b / (2 * a);
    complex = sqrt(descriminant * -1) / (2 * a);

        if (descriminant < 0)
    {
    cout <<"The first Root Value = " << real  << " + " << complex << "i" << endl;
    cout <<"The second Root Value = " << real  << " - " << complex << "i" << endl;
    }
        if (descriminant > 0)
        {
    cout <<"The first Root Value = " << rootvalue1  << endl;          
    cout <<"The second Root Value = " << rootvalue2  << endl;
        }

    return 0;
}

[Sasquadge]

Thanks for your help :)

[mike_2000_17]

Well, it seems you have it solved now. May I suggest you put the calculations of the roots inside the if-else blocks, as so:

descriminant = pow(b,2) - (4 * a * c);
if (descriminant < 0)
{
    real = -b / (2 * a);
    complex = sqrt(descriminant * -1) / (2 * a);
    cout <<"The first Root Value = " << real  << " + " << complex << "i" << endl;
    cout <<"The second Root Value = " << real  << " - " << complex << "i" << endl;
}
else
{
    rootvalue1 = (-b + sqrt(descriminant)) / (2 * a);         
    rootvalue2 = (-b - sqrt(descriminant)) / (2 * a);  
    cout <<"The first Root Value = " << rootvalue1  << endl;          
    cout <<"The second Root Value = " << rootvalue2  << endl;
}

So, this is solved right?

[Sasquadge]

Yes this is solved thank you!

[rubberman]

As usual, mike_2000_17 gives awesome advice! :-) Mike, you have a LOT more patience than I do!