Use Descartes' Rule of Signs to Determine the Possible Number $f ( x ) = - 4 x ^ { 5 } - 8 x ^ { 4 } - 4 x ^ { 3 } + 3 x ^ { 2 } + x + 16$

question 84

Multiple Choice

Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial
function.
- $f ( x ) = - 4 x ^ { 5 } - 8 x ^ { 4 } - 4 x ^ { 3 } + 3 x ^ { 2 } + x + 16$

• A)1 positive zero, 3 or 1 negative zeros
• B)1 positive zero, 4 or 2 negative zeros
• C)1 positive zero, 4 or 2 or 0 negative zeros
• D)1 positive zero, 2 or 0 negative zeros

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Definitions:

Risk-Free Portfolio

An investment portfolio consisting of assets that have no risk of financial loss, typically associated with government bonds.

Portfolio Beta

A measure of the volatility, or systematic risk, of a portfolio in comparison to the market as a whole, indicating how sensitive the portfolio is to market movements.

Security Market Line

A line that represents the relationship between the risk of an investment and its expected return, used in capital asset pricing model (CAPM) to determine risk-adjusted returns.

Unsystematic Risk

The risk associated with a specific company or industry, also known as "diversifiable risk" or "idiosyncratic risk."