Use Descartes' Rule of Signs and the Rational Zeros Theorem $$f ( x ) = 2 x ^ { 3 } + 13 x ^ { 2 } + 10 x + 25$$

question 22

Multiple Choice

Use Descartes' Rule of Signs and the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the
zeros to factor f over the real numbers.
- $$f ( x ) = 2 x ^ { 3 } + 13 x ^ { 2 } + 10 x + 25$$

• A) \(- 1 , \frac { 5 } { 2 } , 5 ; f ( x ) = ( 2 x - 5 ) ( x - 5 ) ( x + 1 )\)
• B) \(- 5 , \frac { 5 } { 2 } , 1 ; f ( x ) = ( 2 x - 5 ) ( x - 1 ) ( x + 5 )\)
• C) \(1 , \frac { 2 } { 5 } , - 5 ; f ( x ) = ( 2 x - 5 ) ( x - 1 ) ( x + 5 )\)
• D) \(- 1 , \frac { 2 } { 5 } , - 5 ; f ( x ) = ( 2 x - 5 ) ( x - 5 ) ( x + 1 )\)

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Definitions:

Expected Rate

The anticipated return or yield on an investment, often based on historical data, current market conditions, and forecasts.

T-bill

Short-term government securities that mature in a year or less, offering investors a safe and liquid means of investment.

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A line on a graph that represents the risk-return trade-off of investments, showing the rates of return for efficient portfolios depending on the risk-free rate and the market risk.

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A statistical measure of the dispersion or variability of a set of data points from their mean, used in finance to gauge the volatility of investment returns.