Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. The polynomial f(x) = x4
- 9x3 - 22x2 has no real zero greater than 8.
1 answer:
Answer:
So f(x) has no real greater than 8. Step - by - step explanation is shown in the attachment.
Step-by-step explanation:
Let f ( x) be a polynomial with real coefficients and with a positive lending coefficient.
If f(x) is divided by x-c and
a) if c>0 and all number in the bottom row of the synthetic division are non negative , then f(x) has no zero greater than c.
b ) if c<0 and the number in the bottom row of the synthetic division alternate in sign then f (x) has no zero less than c
As shown in the figure
Since the number in the bottom row of the synthetic division alternate in sign
So f(x) has no real greater than 8
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Answer:
Step-by-step explanation:
This is the distance formula for cartesian coordinate systems, or your typical xy graph. If given two points to find the distance between, you can assign '1' or '2' to the points, i.e. (1,1) and (2,2) could be: (1,1) is (x1,y1) and (2,2) is (x2,y2). It doesn't matter which point is 1 or 2. If we were to use those example points in this formula, we would have:
We can simplify and come up with:
=
We must remember that square roots can be positive OR negative, HOWEVER, because you are looking for a distance it must be positive .
Hope this helped!