# Problem 29 and 31 lesson 4.6

### B. Bradberry, d. 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. 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."

In order to find the correct answer you must retranslate the problem into the negative version. His error was the sign in front of the x^2.

Descartes rule of signs tells us that there can be either 3 or 1 negative real roots the calculated graph confirms that there is 1 negative root.

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?

solve for h

plug your answer back in to check

The dimensions would be h= 5 b^1=10 and b^2= 14