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

1 Answer
Mar 20, 2016

Answer:

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)#