Question

How do you use the rational roots theorem to find all possible zeros of `f(x)=x^3+x^2-8x-6`?

Answer 1

The Rational Root Theorem states: that the set `(+-1, +-2, +-3, +-6)` constitute the set of all possible zero roots to `f(x)`

Explanation:

Given `f(x) = a_n x^n + a_(n-1)x^(n-1) + cdots+ a_1x6+a_0=Sigma_(i=0)^n a_ix^i`
let `p` and `q` be `AA p: a_0|p` and `q: a_n|q`,
then f(x) potential roots are `x_i: x_i in (p_l/q_k)`
where `p_l` and `q_k` are the `l_(th) and k_(th)` factors

`a_0 = 6 => +-(1, 2, 3, 6)`
`a_3 = 1`
Thus the Rational Root Theorem states:
that the set `(+-1, +-2, +-3, +-6)` constitute the set of all possible zero roots to `f(x)`