# Math III Section 4.6 Problem #29

### J. Jones/2nd period/Kirkland

Your friend is using Descartes's Rule of Signs to figure out 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

If "my friend" from the problem had done this correctly, his work would have looked like this, in the picture above.

This is also what it should have looked like if you had graphed it correctly.

### Math III Section 4.6 #31

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?

These are the steps that you have to do, to get the polynomial to graph it.

This is the equation that you would plug in, and you get to x-intercepts, a negative and a positive. You should take the positive x-intercept and use it as your (h).

Therefore (h)=5, 2h=10 and 2h+4=14.