SOLUTION: Solve the polynomial equation. use rational zero theorem and descarte's rule of signs as a aid in obtaining the first root. 2x^3-17x^2-11x-1=0.

Question 763818: Solve the polynomial equation. use rational zero theorem and descarte's rule of signs as a aid in obtaining the first root.
2x^3-17x^2-11x-1=0.

Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
From left to right, we find one sign change. Number of positive roots can be 1.

Let x = -x, and obtain -2^3-17x^2+11x-1. We find two sign changes, so we may expect 2 or 0 negative roots.

We may like to check negative possible roots, first. They could be -(1/2) and -1.
Omitting much of the synthetic division process here, the only rational root found to work is . The resulting factorization then is this:
.
The quadratic factor is not factorable in just rational numbers. For that factor, roots are and .

ANSWER SUMMARY:
roots are , and and
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