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# Math III Section 4.6 #29 and #31

### V. Edwards, Mr. Kirkland, 12-2-13

"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."

Above is the problem along with the students answer which is wrong. Below i have worked out the problem to get the correct answer.

The correct answer is 3 or 1 negative real roots not just one negative real root.

The student worked out the problem correctly but didn't quit finish. There isn't just one negative real root, there can really be 3 or 1 negative real roots.

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?

First, use a brace map to break down the problem.

Next, you need to find the area of the trapezoid. The formula for finding the area of a trapezoid is A=(1/2)(H)(B1+B2). So the formula for this problem is A=(1/2)(H)(2H+(S+4)).

Do the following steps to find the dimensions of the garden.

The question was, "What dimensions should she use for the garden?". The dimensions she should use are height equals 5, shorter base equals 10, and the longer base equals 14.