SOLUTION: Using Descartes' rule of sign , determine how many positive and negative zeros each of these polynomial functions may have 1. f(x)=-6x^5+x^4+5x^3+x+1 2. f(x)=-6^5+x^4+2x^3-x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Using Descartes' rule of sign , determine how many positive and negative zeros each of these polynomial functions may have 1. f(x)=-6x^5+x^4+5x^3+x+1 2. f(x)=-6^5+x^4+2x^3-x      Log On


   

Question 820949: Using Descartes' rule of sign , determine how many positive and negative zeros each of these polynomial functions may have
1. f(x)=-6x^5+x^4+5x^3+x+1
2. f(x)=-6^5+x^4+2x^3-x+1
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Look just at #1.

As written, you see 1 change in signs.
We expect 1 positive root.

Using %28-x%29 in place of x, obtain -6%28-x%29%5E5%2B%28-x%29%5E4%2B5%28-x%29%5E3%2B%28-x%29%2B1
6x%5E5%2Bx%5E4-5x%5E3-x%2B1
You see 2 changes in sign.
We expect 2 or 0 negative roots.

Know that some roots may be repeated.