The Quadratic Solver

Calculator for the quadratic equation:

0 = ax² + bx + c

a =

b =

c =

The above program will calculate solutions to the quadratic equation.

Enter values for the coefficients a, b, and c.
Click the 'Calculate' button.
The roots of the quadratic equation will pop up.

These values for x are calculated using the solution to the quadratic equation, which is:

the quadratic formula

The derivation of the above equation is available here.

Of course, the coefficient 'a' must be non-zero for this to be a quadratic equation. Solutions are only calculated when a is non-zero.

Click this button to see the actual JavaScript code that executes on this page:

Here's the code that runs when you click the above 'Calculate' button. It is shown here as a possible aid for your study and understanding.

You can change the code, if you like, and then click the following 'Reevaluate code' button. The program will then work as per your changes when you click the 'Calculate' button on the above Quadratic Solver. Of course, your changes, especially random changes, can introduce errors, miscalculations, and browser crashes. If you need to get things back to their original condition, just reload this page using your browser's reload button.

Again, the intention here is to conveniently show you the inner workings of this program so that you understand how the program arrives at the result. Click the 'Code' button again to close this section.

window.calculate = function()
{
	// Variables.
	var a             = 0.0;
	var b             = 0.0;
	var c             = 0.0;	
	var discriminant  = 0.0;
	var x1            = 0.0;
	var x2            = 0.0;
	var realPart      = 0.0;
	var imaginaryPart = 0.0;

	// Get values for a, b, and c.
	a = parseFloat(window.document.aForm.aField.value);
	b = parseFloat(window.document.bForm.bField.value);
	c = parseFloat(window.document.cForm.cField.value);

	// Is this a quadratic equation?
	if(a == 0.0)
	{
		// No, this is not a quadratic equation because a equals zero.
		
		// Tell the world about it.
		alert("Not a quadratic equation. The coefficient 'a' can not be zero.");
	}
	else
	{
		// Yes, this is a quadratic equation because a does not equal zero.
		
		// Calculate the discriminant.
		discriminant = b*b - 4*a*c;

		// Do we have complex conguate roots?
		if(discriminant < 0.0)
		{
			// Yes, we have complex conguate roots.
			realPart      = -b / (2 * a);
			imaginaryPart = Math.sqrt(-discriminant) / (2 * a);			

			// Tell the world about it.
			alert("Discriminant = " + discriminant + "\n\nThe roots are complex conjugates.\n\nx1 = " + realPart + " + " + imaginaryPart + "i" + "\nx2 = " + realPart + " - " + imaginaryPart + "i");
		}
		// Or do we have one real root?
		else if(discriminant == 0.0)
		{
			// Yes, we have one real root.
			x1 = -b / (2 * a);
		
			// Tell the world about it.
			alert("Discriminant = " + discriminant + "\n\nThere is only one real number root.\n\nx = " + x1);
		}
		// We must have two real roots.
		else
		{
			// The real roots.
			x1 = (-b + Math.sqrt(discriminant))/(2*a);
			x2 = (-b - Math.sqrt(discriminant))/(2*a);

			// Tell the world about it.
			alert("Discriminant = " + discriminant + "\n\nThere are two real number roots.\n\nx1 = " + x1 + "\nx2 = " + x2);
		}
	}
}