For this case we have the following function:
f (x) = 2x ^ 2-24x + c
We set zero to find the roots of the function.
We have then:
2x ^ 2-24x + c = 0
x ^ 2-12x + c / 2 = 0
Factoring we have:
(x - / + x1) (x - / + x2) = 0
On the other hand we have:
x2-x1 = 18
x2 + x1 = -12
Solving the system we have:
x1 = -15
x2 = 3
Substituting we have:
(x-15) (x + 3) = 0
Rewriting:
x ^ 2 -12x - 45 = 0
Therefore, the value of c is given by:
c / 2 = -45
c = -90
Answer:
the value of c is:
c = -90