Find the Zeros and Their Multiplicities $$f ( x ) = 3 x ^ { 4 } - 32 x ^ { 3 } + 122 x ^ { 2 } - 188 x + 80$$

question 249

Multiple Choice

Find the zeros and their multiplicities. Consider using Descartes' rule of signs and the upper and lower
bound theorem to limit your search for rational zeros.
- $$f ( x ) = 3 x ^ { 4 } - 32 x ^ { 3 } + 122 x ^ { 2 } - 188 x + 80$$

• A) \(4 , \frac { 2 } { 3 } , \pm 3 i\) (each multiplicity 1 )
• B) \(- 4 , - \frac { 2 } { 3 } , 3 \pm i (\) each multiplicity \(1 )\)
• C) \(- 4 , - \frac { 2 } { 3 } , \pm 3 i\) (each multiplicity 1 \()\)
• D) \(4 , \frac { 2 } { 3 } , 3 \pm i (\) each multiplicity \(1 )\)

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Definitions:

Consumer Surplus

The gap between what consumers are ready and able to expend for a good or service and what they actually spend.

Price Ceiling

A legally imposed limit on the price that can be charged for a good or service, typically set below the equilibrium price.

Excess Demand

A situation where the quantity demanded of a good or service exceeds the quantity supplied at a particular price, often leading to upward pressure on prices.

Consumer Surplus

The disparity between the cumulative amount consumers are willing to pay for a product or service and the amount they actually pay.