# Math III Section 4.6

### H.Winders

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."

**~This is incorrect because when she changes from P(x) to P(-x) she switches the x^2 to -x^2. It should be a positive, because it would have to be a positive you would have 3 sign changes, not 1~ **

1. 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 60ft^2 garden, what dimensions should she use for the garden?

Height=5' Base1= 14' Base2=10'