Solving the Quadratic Equation

**airac13** · September 28th, 2018, 06:31 PM

I'm a complete beginner so I signed up for an edx.com MOOC. I don't think the course is very active anymore so I figured I'd join up here to ask questions when needed. I'm in the process of solving the Quadratic Equation, and I'm not getting the correct results.

the IO is an imported file from the class instructor
Using the numbers a = 5, b = 6, and c = 1
I should get the output of -0.2 and -1.0
I get -0.2 and 0.14833147735478827

Any help?

        double a;
        double b;
        double c;
        double d;
        double first_x;
        double second_x;
 
        IO.output("Enter a: ");
        a = IO.inputDouble( );
        IO.output("Enter b: ");
        b = IO.inputDouble( );
        IO.output("Enter c: ");
        c = IO.inputDouble( );
 
        d = Math.pow(b,2);
        first_x = (-b + Math.sqrt(d - 4 * a * c)) / (2 * a);
        second_x = (-b + Math.sqrt(d + 4 * a * c)) / (2 * a);
 
        IO.outputln("First Solution for x = " + first_x);
        IO.outputln("Second Solution for x = " + second_x);

**jim829** · September 28th, 2018, 10:45 PM

Nothing wrong with your code. It's your math. Your quadratic formula is incorrect. And when you look it up on Wiki, you should check out the computational formula used in programming. It helps avoid overflow issues during intermediate calculations.

Regards,
Jim

**airac13** · September 29th, 2018, 07:24 AM

Originally Posted by jim829

Nothing wrong with your code. It's your math. Your quadratic formula is incorrect. And when you look it up on Wiki, you should check out the computational formula used in programming. It helps avoid overflow issues during intermediate calculations.

Regards,
Jim

Got it, thanks. I made a post saying I still don't see the error, the BOOM it hit me.

Could you still elaborate on the computational formula you mentioned? Didn't find anything referring to that in my search.

Thanks

**jim829** · September 29th, 2018, 09:11 AM

Mea Culpa! I thought it was mentioned in the Wiki. Here is an article on it.

http://people.csail.mit.edu/bkph/art...Quadratics.pdf

Here is a contrived example. Notice that a and b are near their maximum value for a 32 bit integer. So if you add them you will get overflow and in this case, a negative number. Thus the "average" will be a negative number and incorrect. So the trick is to divide first and add the quotients. Computing an average this way is more expensive (i.e. time consuming) since dividing is an expensive operation compared to addition. But in some cases it is required. You can run into similar problems using double values. If you're interesting in understanding how positive and negative integers are stored you can read this -> Two's complement

public class OverFlowDemo {
   public static void main(String[] args) {
 
	  int a = 2_128_928_234;
	  int b = 2_023_192_252;
 
	  System.out.println(a+b);  //overflow - the sum won't fit in an int.  
	  System.out.println((a + b)/2);  // normal averaging - wrong answer
 
	  System.out.println();
	  System.out.println(a/2);  // so divide first, then add
	  System.out.println(b/2);
 
	  System.out.println(a/2 + b/2);  //alternate way - correct answer
   }
}

Note: The above is not really a Java issue but is germane to computer science and many programming languages and computer architectures.

Regards,
Jim

**hend_** · December 11th, 2023, 11:20 AM

Your code is fine, and also formula is fine.

you only have missed some +/- places
you should set:
+ Math.sqrt(d - 4 * a * c)
- Math.sqrt(d - 4 * a * c)
instead of:
+ Math.sqrt(d - 4 * a * c)
+ Math.sqrt(d + 4 * a * c)

**Norm** · December 11th, 2023, 11:56 AM

The thread is 5 years old. I doubt any of the previous posters will be back to read this.

**hend_** · December 11th, 2023, 12:51 PM

I've lately noticed that but maybe others who would start this course would search for the answer as I did, so the reply may benefit them

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