Mathematica Solving Real Roots with NSolve and Plotting a Bifurcation Diagram

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To find only the real roots using NSolve in Mathematica, the function Cases can be applied to filter the results, as demonstrated in the provided example. The command "Cases[x /. NSolve[(x - 1)(x^2 + 3)(x^4 + 5) == 0, x], _Real]" successfully extracts the real root, which is 1. For plotting a bifurcation diagram, users are encouraged to explore specific functions or resources that facilitate this visualization. A link to relevant bifurcation resources is shared for further assistance. The discussion focuses on effectively isolating real roots and generating bifurcation diagrams in Mathematica.
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Hi, I'm using NSolve in Mathematica but I only want to find the roots that are real numbers as my answer gives a lot of imaginary numbers. How can I do this?

I want to then plot a birfucation diagram using a table of data. Is there a function to do this?

Thanks!
 
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In[1]:=x /. NSolve[(x - 1)(x^2 + 3)(x^4 + 5) == 0, x]
Out[1]={-1.05737 - 1.05737*I, -1.05737 + 1.05737*I, -3.81167*^-27 - 1.73205*I,
-3.81167*^-27 + 1.73205*I, 1., 1.05737 - 1.05737*I, 1.05737 + 1.05737*I}

In[2]:=Cases[x /. NSolve[(x - 1)(x^2 + 3)(x^4 + 5) == 0, x], _Real]
Out[2]={1.}

http://search.wolfram.com/?query=bifurcation&x=5&y=4
 

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