<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>