# Math III Section 4.6 #29 and #31

### Denysia Wright

Core 2

Problem #29- Negative Real Roots

This is the problem that we are given to correct from problem #29. Sooo, lets get started!!!!

In order to solve for negative real roots, we have to have negatives, correct? Correct. So here in the photo above, we substituted {P(-x)} for all of the places that had an x as the variable.

In the photo above we simply simplified, the problem, and here we were able to identify the sign changes, and the negative real roots!!!

Here is the Original problem, that is wrong. As you can see, whoever did this problem only has one sign change when it should be three. They have this wrong because, they did not simplify correctly. But thanks to us, we fixed it for them!!!!!

## Problem #31 - Trapezoid Garden

In the photo above, I have made a brace map from the word problem that was given to us, in problem #31, that only has the important details. This is actually considered our starting point... Soooo, let's get started!!!!

From the previous photo, we learned that whoever was building this Trapezoid Garden, wanted the shorter base to be two times the height, and the longer base four more than the shorter base. So here is where we made our equation, and we basically plugged everything in according to the way it was given. We were also given the option to factor out the equation, or use the Quadratic Formula.

As you can see in the photo above, we chose to solve this problem by using the Quadratic Formula, which is -b+/- the square root of b^2-4ac. And here, we simply plugged the equation h^2+h-30 into the quadratic formula. When the formula was completed, you saw that we had two answers, 5, and -6. Wonder why we chose five? Scrool down to the next photo to find out!!

We chose 5 to be our answer, because the base of the garden, could NOT be a negative... why not? It wouldn't have made since.. So the dimensions she could use for the garden are: 2(5) , and 2(5)+4.