Find All Rational, Irrational, and Complex Zeros $P ( x ) = x ^ { 4 } - 81$

question 32

Multiple Choice

Find all rational, irrational, and complex zeros. $P ( x ) = x ^ { 4 } - 81$

• A) \(\{ - 3,3 , - 3 i , 3 i \}\)
• B) \(\{ - 3,3 \}\)
• C) \(\{ 3 \}\)
• D) \(( - 3 i , 3 i \}\)
• E) \(\{ - 9,9 , - 3 i , 3 i \}\)

---

Definitions:

Consumption

The consumption of products and services by individuals in a household.

Impossibility Theorem

A proposition demonstrated by Kenneth Arrow showing that no system of aggregating individual preferences into social decisions will always yield consistent, nonarbitrary results.

Voting Paradox

A simple demonstration of how majority-rule voting can lead to seemingly contradictory and inconsistent results. A commonly cited illustration of the kind of inconsistency described in the impossibility theorem.

Social Choice

The problem of deciding what society wants. The process of adding up individual preferences to make a choice for society as a whole.