Question

How do you use the rational root theorem to find the roots of `2x^3 - 9x^2 - 11x +8 = 0`?

Answer 1

If `p/q` is a root of `2x^3-9x^2-11x+8=0` expressed in lowest terms, then `p` is a divisor of the constant term `8` and `q` is a divisor of the coefficient `2` of the highest order term.

So if this polynomial has rational roots, they must be one of the following:

`-8`, `-4`, `-2`, `-1`, `-1/2`, `1/2`, `1`, `2`, `4` or `8`.

Unfortunately, none of these is a root, so this cubic has no rational roots and the rational root theorem cannot help us find the roots it does have.