Condition for positive"RooBernstein"!

Dear Experts,
I would like to use the class "RooBernstein"
The Bernstein polynomials are supposed to be always positive in the interval [0,1]
From the web page ( root.cern.ch/root/html/RooBernstein.html ) I perfectly
understand the comment : “In this implementation, we extend [0,1] to be the range of the parameter”

Bu my question is: what range shall I give to the coefficients in order to have a polynomial
which is always positive ?

Let’s take the simple example of degree 1:
B0,1 = t
B1,1 = (1-t)

Btotal = aB0,1 + bB1,1 = at + b(1-t) = b + (a-b)*t
which is always positive in the interval [0,1] only if:
b > 0
and
a > b
Do I need to put these conditions myself ? Or somehow they are already implemented ?

Thanks,

  • Mauro.