Word Problem #29 and #31 from 4.6 Homework

H. Brantley in Mr. Kirkland's Math III Class


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

Because there are 3 sign changes in P(-x) there must be 3 or 1 negative real roots.

There is one negative real root, and no real roots for the positives.


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?

After solving for "H", I plugged it into the dimensions. I came out with 5 being the height, 10 being the short base, and 14 being the longer base.

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