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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