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.

Algebra ->  Polynomials-and-rational-expressions -> 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.       Log On


   

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(39617) About Me  (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 highlight%28-%281%2F2%29%29. The resulting factorization then is this:
highlight%282%28x%2B1%2F2%29%28x%5E2-9x%2B1%29=0%29.
The quadratic factor is not factorable in just rational numbers. For that factor, roots are 9%2F2-%281%2F2%29%2Asqrt%2877%29 and 9%2F2%2B%281%2F2%29%2Asqrt%2877%29.

ANSWER SUMMARY:
roots are -1%2F2, and 9%2F2-%281%2F2%29%2Asqrt%2877%29 and 9%2F2%2B%281%2F2%29%2Asqrt%2877%29