20.3 Example Program: Roots of a Polynomial

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NOTE: This program is in the file complx.cpp .

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The roots of a polynomial a x2 + b x + c = 0 are given by the formula:

x = (-b 2 - 4ac))/2a

The following program takes as input three double precision numbers, and returns the complex roots as a pair of values.

typedef complex<double> dcomplex;

pair<dcomplex, dcomplex> quadratic
      (dcomplex a, dcomplex b, dcomplex c)
         // return the roots of a quadratic equation
{
   dcomplex root = sqrt(b * b - 4.0 * a * c);
   a *= 2.0;
   return make_pair(
      (-b + root)/a, 
      (-b - root)/a);
}