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# 4.6 Word Problems

A. Moore Math III 1st Period

#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

Since there was no sign changes, there are no positive real roots.

Since there are three sign changes, there are three possible negative real roots or three minus an even number (two), which would be one possible negative real root.

#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?

Once you created the quadratic equation, you graph it.  Since you are trying to find "h", the solution (zero), will be "h".  Then, you plug the positive solution (5) into the equations for the two bases.  The result is that she can build a garden with a height of 5 ft, base 1 length of 10 ft, and a base 2 length of 14 ft.