For the last part you are looking for the solutions to:

or:

Decartes rule of signs tells us this has or positive real roots. As the function changes sign between and there is at least one root in this interval.

Now:

Examining the discriminant of the quadratic we find this has no real zeros, and as this is positive for large , the cubic is everywhere an increasing function, and so can have at most one zero, which we have already located between and .

RonL