Math III Section 4.6 Numbers 29 and 31
Holly Radford

#29 Problem

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.

The Work Solved
The Answer

#31 Problem

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 60 ft^2 garden, what dimensions should she use for the garden?

The Brace Map
Diagram
Work and Answer