MATLAB problem: A) Write a MATLAB function that computes the roots of f(x) = ax

Question

MATLAB problem:

A) Write a MATLAB function that computes the roots of f(x) = ax2 + bx + c, where a, b, and c are real constants.

Write the function call as [x1,x2] = quadroots(a,b,c) where x1 and x2 are the two roots. Make sure to minimize

the effect of loss of significance, and use as few arithmetic operations as possible.

B) Write the script file that computes your function for both f(x) = x2 - 105 x + 1 and f(x) = x2 + 105 x + 1, and test

it by computing both f(x1) and f(x2) for both functions.

Explanation / Answer

A.
MATLAB function that computes the roots of f(x) = ax2 + bx + c, where a, b, and c are real constants

PROGRAM:

function [r1r,r1i,r2r,r2i] = quadric   ( a,b,c,opt );

        % -------------------- implementation   ----------------------
        small = 0.00000001;
        r1r = 0.0;
        r1i = 0.0;
        r2r = 0.0;
        r2i = 0.0;

        discrim = b*b - 4.0 *a*c;
%a
%b
%c
%discrim
        % --------------------- real roots --------------------------
        if ( abs(discrim) < small )
            r1r = -b / ( 2.0 *a );
            r2r = r1r;
%            if (opt=='U')
%                r2r = 99999.9;
%              end;
          else
            if abs(a) < small
                 r1r = -c/b;
              else
            if ( discrim > 0.0 )
                r1r = ( -b + sqrt(discrim) ) / ( 2.0 *a );
                r2r = ( -b - sqrt(discrim) ) / ( 2.0 *a );
              else
                % ------------------ complex roots --------------------
                if (opt=='I')
                    r1r = -b / ( 2.0 *a );
                    r2r = r1r;
                    r1i = sqrt(-discrim) / ( 2.0 *a );
                    r2i = -sqrt(-discrim) / ( 2.0 *a );
                  else
                    r1r = 99999.9;
                    r2r = 99999.9;
                  end;
              end;
            end;
          end;

b.

function r = quadroot(p)
   % Check array class.
   if ~isnumeric(p)
      error('P must be a numeric array.');
   end

   % Check array size.
   if (ndims(p) ~= 2) | (size(p, 1) ~= 1)
      error('P must be row vector.');
   end

   a = p(1);
   b = p(2);
   c = p(3);

   if a == 0
      if b == 0
         if c == 0
            %
            % a, b, c are zero: 0 = 0
            %
            error('All coefficients are zero');
         else
            %
            % a, b are zero: c = 0;
            %
            error('Constant equation');
         end
      else
         if c == 0
            %
            % a, c are zero: b*x = 0
            %
            r = 0;
            return;
         else
            %
            % a is zero: b*x + c = 0
            %
            r = -c/b;
            return;
         end
      end
   else
      if b == 0
         if c == 0
            %
            % b, c are zero: a*x^2 = 0
            %
            r = [0 0];
            return;
         else
            %
            % b is zero: a*x^2 + c = 0
            %
            t = sqrt(c/a);
            r = [t -t];
            return;
         end
      else
         if c == 0
            %
            % c is zero: a*x^2 + b*x = 0;
            %
            r = [0 -b/a];
            return;
         else
            %
            % none of a, b, c are zero: a*x^2 + b*x + c = 0
            %
            d = b*b - 4*a*c;    % discriminant
            if d == 0
               % two identical roots
               t = -b/(2*a);
               r = [t t];
               return;
            else
               if sign(real(sqrt(d))) == sign(real(b))
                  t = -b - sqrt(d);
               else
                  t = -b + sqrt(d);
               end
               r = [ t/(2*a) (2*c)/t ];
               return;
            end
         end
      end
   end
   % we should never get here
   error('Internal error');
end

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