Answer:
between 2 and 3
Step-by-step explanation:
Positive rational roots will be one of 1, 3, or 9. The sum of coefficients is ...
-1 -1 +4 +9 = 11
this tells us the root is greater than 1.
We can try f(3) to see if that is a root:
f(3) = ((-3 -1)(3)+4)(3) +9 = (-12 +4)(3) +9 = -24 +9 = -15
This tells us the root is between 1 and 3. In order to narrow it further, we need to find f(2).
f(2) = ((-2 -1)(2) +4)(2) +9 = (-6 +4)(2) +9 = 5
The sign of the function changes between f(2) > 0 and f(3) < 0, so the root is between the integer values 2 and 3.
__
Additional comment
An iterative solution finds the irrational root to be near 2.34417122935.
