Question

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.

Answer 1

So f(x) has no real greater than 8. Step - by - step explanation is shown in the attachment.

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