# Math III Section 4.6 #29 and #31

### John are. Arrington, Kirkland

# #29

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

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."

* This is wrong because she changed x^2 to -x^2. It should be positive and if it was positive it would have 3 sign changes not 1. *

## #31

A gardener is designing a new garden in the shape of a trapezoid. She wants the shorter base to be twice the height and the longer base to be 4 feet longer than the shorter base. If she has enough topsoil to create a 6oft^2 garden, what dimensions should she use for the garden?

h=5 b1=14 b2=10