First we need to know the coordinates of the movie theater, we can do this applying the midpoint formula:
We have that the movie theater is located at (2,4). Now we use this coordinates to find the location of Clara's house using again the midpoint formula:
Therefore, Clara's house is located at (-2,0)
Using Vieta's Theorem, it is found that c = 72.
<h3>What is the Vieta Theorem?</h3>The Theorem states that:
In this problem, the polynomial is:
Hence the coefficients are .
Since the difference of the solutions is 1, we have that:
Then, from the first equation of the Theorem:
Now, from the second equation:
To learn more about Vieta's Theorem, you can take a look at brainly.com/question/23509978