Give the Maximum Number of Zeros the Polynomial Function May $$f ( x ) = - 2 x ^ { 5 } + x ^ { 3 } - x ^ { 2 } + 3$$

question 332

Multiple Choice

Give the maximum number of zeros the polynomial function may have. Use Descarte's Rule of Signs to determine how
many positive and how many negative zeros it may have.
- $$f ( x ) = - 2 x ^ { 5 } + x ^ { 3 } - x ^ { 2 } + 3$$

• A) 5 ; 3 or 1 positive zeros; 2 or 0 negative zeros
• B) 5 ; 2 or 0 positive zeros; 2 or 0 negative zeros
• C) 5 ; 3 or 1 positive zeros; 3 or 1 negative zeros
• D) \(5 ; 2\) or 0 positive zeros; 3 or 1 negative zeros

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Definitions:

Relevant Risk

The portion of an investment's risk that cannot be eliminated through diversification, also known as systematic or market risk.

Market Portfolio

A theoretical portfolio of all assets in the market, with each asset weighted according to its market capitalization.

Efficient Frontier

A concept in modern portfolio theory which represents a set of optimal portfolios that provide the highest expected return for a defined level of risk or the lowest risk for a given level of expected return.

Indifference Curve

A curve connecting all portfolios with the same utility according to their means and standard deviations.