**Write a program that receives the coefficients of a quadratic equation and returns its roots, even complex ones, through dialog boxes.**

### Step 1: Receiving the coefficients of the quadratic equation

First the program receives user data, which are the coefficients of equation 3, 'a', 'b' and 'c':ax ² + bx + c = 0

## Step 2: Checking if 'a' coefficient is not 0

An equation of the second degree is only the second degree if 'a' is different from 0.If the user enters the value 0, the program enters a loop until the user enters a value other than 0.

## Step 3: Checking if the delta is positive and show the real roots

If delta is greater than or equal to 0 the roots are real and are easily calculated by the quadratic formula.

## Step 3: Checking if the delta is negative and show the complex roots

If not, the roots will be complex.

To calculate the complex roots do be positive delta (-delta), took its root and calculate separately the real and imaginary part.

Java code of how to to a graphical application that show the roots of a quadratic equation:

```
import javax.swing.JOptionPane;
public class bhaskara_dialogBoxes {
public static float delta(float a, float b, float c){
return (b*b - 4*a*c);
}
public static void main(String[] args){
String value, roots;
float a=0, b, c, //coefficients
delta, //delta
sqrtdelta, //delta square root
root1,root2; //roots
//STEP 1: receive the coefficients
value = JOptionPane.showInputDialog("Enter the 'a' value: ");
a = Float.parseFloat(value.trim());
value = JOptionPane.showInputDialog("Enter the 'b' value:");
b = Float.parseFloat(value.trim());
value = JOptionPane.showInputDialog("Enter the 'c' value:");
c = Float.parseFloat(value.trim());
//STEP 2: check if 'a' if not 0
while(a==0){
if(a==0){
value = JOptionPane.showInputDialog("'a' can't be 0. Insert other value");
a = Float.parseFloat(value.trim());
}
}
//STEP 3: check if delta is positive. If it is, show the real roots
if(delta(a,b,c)>=0){
root1 = (-b + (float)Math.sqrt(delta(a,b,c)))/(2*a);
root2 = (-b - (float)Math.sqrt(delta(a,b,c)))/(2*a);
roots = String.format("The roots are: %.2f e %.2f", root1, root2);
JOptionPane.showMessageDialog(null,roots);
//STEP 4: if delta is negative, we should format the output to show the complex roots
} else {
roots = String.format("The roots are:\n" +
"%.2f + %.2fi\n" +
"%.2f - %.2fi",(-b/(2*a)), ( (float)Math.sqrt(-delta(a,b,c) ) / (2*a) )
,(-b/(2*a)), ( (float)Math.sqrt(-delta(a,b,c) ) / (2*a) )
);
JOptionPane.showMessageDialog(null,roots);
}
}
}
```

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