# Math III Section 4.6 #29 and #31

### E. Collins

"Your friend is using Descartes's Rule of Signs to find the number of negative real roots of x^3 + x^2 + x + 1 = 0. Describe and correct the error."

"P(-x) = (-x)^3 +(-x)^2 + (-x) +1

= -x^3 - x^2 - x +1"

"Because there is only one sign change in P(-x), there must be one negative real root."

Answer: "Because there are three sign changes in P9-x), there must be three and/or one negative real root."