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Mrac [35]
3 years ago
15

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.

Mathematics
1 answer:
7nadin3 [17]3 years ago
6 0

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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