Use the Boundedness Theorem to Determine Whether the Polynomial Function $f ( x ) = x ^ { 5 } + 10 x ^ { 4 } - 25 x ^ { 3 } - 10 x ^ { 2 } + 24 x$

question 139

Multiple Choice

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition.
-The polynomial f(x) $f ( x ) = x ^ { 5 } + 10 x ^ { 4 } - 25 x ^ { 3 } - 10 x ^ { 2 } + 24 x$ has no real zero less than -8.

• A) Yes, the boundedness theorem shows that the polynomial has no real zero less than -8.
• B) No, the boundedness theorem does not show that the polynomial has no real zero less than -8.

---

Definitions:

Satisfaction

The feeling of pleasure or fulfillment that comes from meeting one's needs or expectations.

Real Wages

Wages adjusted for inflation, reflecting the actual purchasing power of income.

Opportunity Cost

Opportunity cost represents the value of the best alternative that must be forgone as a result of choosing a particular action or decision over others.

Labor-saving Devices

Tools, machines, or systems that reduce the amount of labor needed to perform a task or produce a good.