# Question:RootFinding:-Parametric to isolate real roots of a polynomial?

## Question:RootFinding:-Parametric to isolate real roots of a polynomial?

Maple

In relation to my comment below:
https://www.mapleprimes.com/questions/238277-Robustness-Of-Plotevalsomething#comment301920 (whose my worksheet rho-analysis_mmcdara_Gammapositive_MaPal.mw builds on the Sturm's analysis of @mmcdara)

I would like to better understand how to isolate/pin down the 4 real roots whose existence was confirmed by Sturm's analysis. To do so, @acer suggested to look into RootFinding:-Parametric: rho-analysis_acc(1).mw
Questions:

1. Why the plot doesn't change if I also include -1<rho and rho<1 among the equations to solve? I understood that regions 1, 4 and 5 have 0 solutions anyway but if I add the constraints on rho I should expect 2 regions instead of 5, right?

2. I don't understand SampleSolutions(m,2)=0.56 and SampleSolutions(m,3)=0.51 (even after reading help page). How are these numeric values found?

3. Looking at the big picture, how to reconcile this CellPlot with A) my plot3d of Eq in https://www.mapleprimes.com/questions/238277-Robustness-Of-Plotevalsomething#comment301920 and B) @mmcdara Sturm's analysis. I am having a hard time putting all together.

Thank you.

EDIT: I formulated this question by branching out from my comment