Here is a picture with the answer.
Answer: Ix - 5I ≥ 5.
Step-by-step explanation:
We want the set:
[0, 10]
to be the solution of:
Ix - bI ≤ c
So we need to find the values of c and b.
The first step is to find the middle point in our segment.
We can do that by adding the extremes and dividing it by 2.
M = (10 + 0)/2 = 5
And we also want to find half of the difference between the extremes, this is:
D = (10 - 0)/2 = 5.
Now, this set will be the set of solutions of:
Ix - MI ≥ D
Then in our case, we have:
Ix - 5I ≥ 5.
so we have that b = 5, and c = 5.
So -5x=-50
multiply both sides by -1
5x=50
divide by 5
x=10
check
-5 times 10=-50
-50=-50
check
Let's pick an arbitrary value of 5.
Let's pick another arbitrary value: 1
Between these two values, the polynomial is continuous. This means for the two polynomial points to be satisfied, there must be
at least one root between these two points.
We can either use the Intermediate Value Theorem or Newton's method to make a better approximation from there.