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My only goal is to plot the x-intercepts and display their coordinates; however, there is an additional point being added to the first quadrant and the y-value for point a is not zero. How and why?

f[x_] := x^5 - 2 x^3 + 1
points = NSolve[f[x] == 0, x, Reals]
Plot[f@x, {x, -2, 2}, MeshFunctions -> {f@# &}, Mesh -> {{0}}, 
    MeshStyle -> Directive[Red, PointSize[Large]]]

Mathematica graphics

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    $\begingroup$ If you do PlotRange->All the extra point goes away. I assume this is an artifact of Automatic pre-processing your data. You can probably find details in the docs. You could use the option Epilog->{Red,PointSize[Large],Point/@points}, then you don't have to worry about Mesh behaving. $\endgroup$
    – N.J.Evans
    Commented Sep 30, 2015 at 20:02

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