Book1 Listing 35: Possible sphere intersection logic error

[theAnuragMishra]

After introducing theInterval class, the intersection code is updated to

if (!ray_t.surrounds(root)) {
            root = (h + sqrtd) / a;
            if (!ray_t.surrounds(root))
                return false;
        }

Shouldn't it use contains instead though?
The given code rejects a root that is equal to t_min or t_max.

Well while writing this I went to the book again and saw it rejects such roots before introducing the Interval class too. But again the meaning of t_min or t_max to me is that they are inside the acceptable value boundary. t_min or minimum time sounds like the minimum acceptable value of time.