For loop only once

Hi i want get root of equation.

but my script shows many same roots. i want show like function roots.

how can i do more?

 clc
 clear
 pre_x1=0;

 x2=[];

 eps = 1e-9;

 for n = -100:1:100

     options = optimset('Display', 'off');

     x1 = fzero('x^3 -6*x^2 + 11*x -6',n,options);

     if (isnan(x1) == 0 && pre_x1 ~= x1)
       % fprintf('guess = %5d, sol=%f10.n\n',n,x1);
       if x1 == x1
          pre_x1 = x1;
          x2(end+1) = x1;
       end
     end
 end

 x2

 roots([1 -6 11 -6])

Answer 1

[Geoff Hayes]

You have the correct idea but have to remember that you cannot compare floating precision numbers using the equality (or negation of it). The

 pre_x1 ~= x1

would be fine if both of these variables are integers but when it comes to floating-point numbers, you should use something more like

 abs(pre_x1-x1)>eps

In the above, we consider the difference between the two numbers, and if they are greater than epsilon (note that eps is a built-in function) then the two are different. So using this will cut down on the number of duplicate roots.

Unfortunately, you can't assume that the roots will always be ordered so you will have to review the list of all found roots rather than just the previous one. So your code becomes

 if ~isnan(x1)
     % indicator as to whether a duplicated root has been found (true)
     % or not (false)
     dupRootFound = false;

     % loop through all roots found so far
     for k=1:length(x2)
         if abs(x2(k)-x1)<eps
             % a duplicated root has been found so exit
             dupRootFound=true;
             break;
         end
     end
     if ~dupRootFound
         % no duplicated root found so add it
         x2 = [x2 x1];
     end
 end

Just replace your if block with the above and see what happens!

[a]

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