Use Descartes' Rule of Signs to Determine the Possible Number $$f ( x ) = 3 x ^ { 6 } - 7 x ^ { 4 } - 7 x ^ { 3 } + 4 x ^ { 2 } - 5 x$$

question 59

Multiple Choice

Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative
real zeros for the function.
- $$f ( x ) = 3 x ^ { 6 } - 7 x ^ { 4 } - 7 x ^ { 3 } + 4 x ^ { 2 } - 5 x$$

• A)
• \(\begin{array}{c|c|c}
• \text { Positive } & \text { Negative } & \text { Nonreal Complex } \\
• \hline 2 & 3 & 1 \\
• 2 & 1 & 3 \\
• 0 & 3 & 3 \\
• 0 & 1 & 5
• \end{array}\)
• B)
• \(\begin{array}{c|c|c}
• \text { Positive } & \text { Negative } & \text { Nonreal Complex } \\
• \hline 3 & 2 & 1 \\
• 3 & 0 & 3 \\
• 1 & 2 & 3 \\
• 1 & 0 & 5
• \end{array}\)
• C)
• \(\begin{array}{c|c|c}
• \text { Positive } & \text { Negative } & \text { Nonreal Complex } \\
• \hline 2 & 0 & 4 \\
• 0 & 0 & 6
• \end{array}\)
• D)
• \(\begin{array}{c|c|c}
• \text { Positive } & \text { Negative } & \text { Nonreal Complex } \\
• \hline 3 & 2 & 1 \\
• 1 & 2 & 3
• \end{array}\)

---

Definitions:

World Cup

An international football (soccer) competition held every four years among the national teams of FIFA member countries.

Behavioral Economists

Economists who study the impacts of psychological, cognitive, emotional, cultural, and social factors on economic decisions made by individuals and institutions.

Behavioral Economics

An area of economics that incorporates insights from psychology to understand decision-making and economic behavior that deviates from classical economic theories.