Question 174594
First, look at the factors of your first and last coefficients:

Factors of 1: +- 1
Factors of -3: +- 1, +- 3

When you have a cubic equation, any rational roots (if they exist) can be found by the quotient of the last coefficient's factors divided by the first coefficient's factors.  For example, possible choices here are:

+-1, +-3

You can try those 4 and you'll find they aren't roots so there are no rational roots.

Now, consider this:

f(1) = -1
f(2) = 9

Obviously the function has a zero between 1 and 2 because the sign switches from positive to negative!  We know this root isn't rational so there is an irrational root within this interval.