Is there a way to find a missing cubic root if a maximum turning point and a turning point on the x axis is known? The maximum turning point is at (50,30) while the turning point root is (100,0)
So in this equation
F(x) = (x+a)(x-100)(x-100)
I need to find knowing that the given points are stat points with a gradient of zero.
Thank you
In the answer to Finding cubic function from points?, you already were given the full factorization leading to the third root at $x=25$.
In your product you are missing the overall scaling factor, as the extremal point $(50,30)$ imposes two conditions necessitating two degrees of freedom.