<h2>

**11. Find discriminant.**</h2>

**Answer:** D) 0, one real solution

A** quadratic function** is given of the form:

We can find the roots of this equation using the **quadratic formula:**

Where is named the **discriminant. **This gives us information about the roots without computing them. So, arranging our equation we have:

**<em>Since the discriminant equals zero, then we just have one real solution.</em>**

<h2>

**12. Find discriminant.**</h2>

**Answer:** D) -220, no real solution

In this exercise, we have the following equation:

So we need to arrange this equation in the form:

Thus:

So the discriminant is:

<em>**Since the discriminant is less than one, then there is no any real solution**</em>

<h2>13. Value that completes the squares</h2>

**Answer: **C) 144

What we need to find is the value of such that:

is a **perfect square trinomial, **that are given of the form:

and can be expressed in **squared-binomial **form as:

So we can write our quadratic equation as follows:

Finally, the value of that completes the square is 144 because:

<h2>14. Value that completes the square.</h2>

**Answer: **C)

What we need to find is the value of such that:

So we can write our quadratic equation as follows:

Finally, the value of that completes the square is because:

<h2 /><h2>15. Rectangle.</h2>

In this problem, we need to find the length and width of a rectangle. We are given the area of the rectangle, which is 45 square inches. We know that the formula of the area of a rectangle is:

From the statement we know that** the length of the rectangle is is one inch less than twice the width, this can be written as:**

So we can introduce this into the equation of the area, hence:

The only valid option is because is greater than zero. Recall that we can't have a negative value of the width. For the length we have:

Finally:

<h2>16. Satellite</h2>

The distance in miles between mars and a satellite is given by the equation:

where is the number of hours it has fallen. So we need to find when the satellite will be 452 miles away from mars, that is, :

Finally, <em>**the satellite will be 452 miles away from mars in 6 hours.**</em>