A Polynomial F ( X ) with Real Coefficients and Leading

question 1

Multiple Choice

A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f ( x ) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R. $4 + 1 i , - 9 + i \text {; degree } 4$

• A) \(\left( x ^ { 2 } - 8 x + 17 \right) \left( x ^ { 2 } + 18 x + 82 \right)\)
• B) \(\left( x ^ { 2 } - 8 x + 16 \right) \left( x ^ { 2 } + 18 x + 81 \right)\)
• C) \(\left( x ^ { 2 } - 8 x + 81 \right) \left( x ^ { 2 } + 18 x + 17 \right)\)
• D) \(\left( x ^ { 2 } - 8 x + 17 \right) \left( x ^ { 2 } + 18 x + 16 \right)\)
• E) \(\left( x ^ { 2 } - 8 x + 16 \right) \left( x ^ { 2 } + 18 x + 82 \right)\)

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Definitions:

Monopolist

An entity that is the sole provider of a particular product or service in the market, having significant control over pricing.

Deadweight Loss

A loss of economic efficiency that can occur when the free market equilibrium for a good or a service is not achieved.

Society's Welfare

The overall well-being and quality of life of the people within a society, including factors like health, happiness, and economic prosperity.

Socially Efficient

A market condition where resources are allocated in a way that maximizes the overall benefit to society.