Cubic equation solver

Input Variables

Output Variables

Program Code

Description

Variable Name *	(dynamic type) * !	UP Down Delete
Default Value *	*
Description *	*
Multi Lines

Variable Name *	(dynamic type) * !	UP Down Delete
Default Value *	*
Description *	*
Multi Lines

Variable Name *	(dynamic type) * !	UP Down Delete
Default Value *	*
Description *	*
Multi Lines

Variable Name *	(dynamic type) * !	UP Down Delete
Default Value *	*
Description *	*
Multi Lines

Variable Name *	(dynamic type) *	UP Down Delete
Description *	*	UP Down Delete

Variable Name *	(dynamic type) *	UP Down Delete
Description *	*	UP Down Delete

Variable Name *	(dynamic type) *	UP Down Delete
Description *	*	UP Down Delete

Input Variables List

Output Variables List

Source Code

double m = 27 * Math.Pow(a * d ,2) - 18 * a * b * c * d  + 4 * a * Math.Pow(c,3) + 4 * Math.Pow(b,3) * d - Math.Pow(b * c,2);
if (a == 0)
{
   x1 = "a can not be zero";
   x2 = "a can not be zero";
   x3 = "a can not be zero";
}
else
{
   double z = 13.5 * a * a * d - 4.5 * a * b * c + Math.Pow(b,3);
   if (Math.Abs(m) < 1e-9)
   {
      if (Math.Abs(z) < 1e-12)
         x1 = x2 = x3 = -b / 3.0 / a;
      else
      {
         z = z < 0 ? -Math.Pow(-z,1.0/3):Math.Pow(z,1.0/3);
         x1 = (-b - 2 * z) / 3 / a;
         x2 = x3 = (-b + z) / 3 / a;
      }
   }
   else if (m < 0)
   {
      double th = Math.Acos(-z / (Math.Sqrt(-27 * Math.Pow(a * c,3) + 27 * Math.Pow(a * b * c,2) - 9 * a * Math.Pow(b,4) * c + Math.Pow(b,6)))) / 3;
      x1 = (-b + 2 * Math.Sqrt(b * b - 3 * a * c) * Math.Cos(th)) / 3 / a;
      x2 = (-b + 2 * Math.Sqrt(b * b - 3 * a * c) * Math.Cos(th + 2 * Math.PI / 3)) / 3 / a;
      x3 = (-b + 2 * Math.Sqrt(b * b - 3 * a * c) * Math.Cos(th + 4 * Math.PI / 3)) / 3 / a;
   }
   else
   {
      string i;
      double r1 = z + Math.Sqrt(z * z - Math.Pow(b * b - 3 * a * c,3));
      double r2 = z - Math.Sqrt(z * z - Math.Pow(b * b - 3 * a * c,3));
      r1 = r1 < 0 ? -Math.Pow(-r1,1.0/3):Math.Pow(r1,1.0/3);
      r2 = r2 < 0 ? -Math.Pow(-r2,1.0/3):Math.Pow(r2,1.0/3);
      x1 = (-b - r1 - r2) / 3 / a;
      double r = (-b + (r1 + r2) / 2) / 3 / a;
      if (Math.Abs(Math.Abs((r1 - r2) / Math.Sqrt(3) / 2 / a) - 1) < 1e-12)
         i = "";
      else
         i = Convert.ToString(Math.Abs((r1 - r2) / Math.Sqrt(3) / 2 / a));
      if (Math.Abs(r) < 1e-12)
     {
        x2 = i + "i";
        x3 = "-" + i + "i";
     }
     else
     {
         x2 = Convert.ToString(r) + " + " + i+ "i";
         x3 = Convert.ToString(r) + " - " + i + "i";
      }
   }
}

Subject

Description

This program calculates the three roots of the cubic equation:
ax³ + bx² + cx + d = 0

Category Mathematics

Created By zizo0003

Created Date 5/1/2011

Last Modify Date 5/1/2011

Calculation Count 20

Version 1.00

Positive 0

Neutral 0

Negative 0

Related Program ID 147 , 146