Use the Rational Zero Theorem to List All Possible Rational $$f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 2 } - 2 x + 6$$

question 250

Multiple Choice

Use the Rational Zero Theorem to list all possible rational zeros for the given function.
- $$f ( x ) = - 4 x ^ { 4 } + 3 x ^ { 2 } - 2 x + 6$$

• A) \(\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6\)
• B) \(\pm \frac { 1 } { 6 } , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 2 } { 3 } , \pm \frac { 4 } { 3 } , \pm 1 , \pm 2 , \pm 4\)
• C) \(\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6\)
• D) \(\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm \frac { 2 } { 3 } , \pm \frac { 3 } { 4 } , \pm \frac { 3 } { 2 } , \pm 1 , \pm 2 , \pm 3 , \pm 6\)

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Definitions:

Return on Assets

An indicator of how profitable a company is relative to its total assets, calculated as net income divided by total assets.

M&M Proposition II

A theory proposing that the value of a firm is unaffected by its capital structure, assuming no taxes and that investment returns are required to increase with leverage.

Cost of Equity

The rate of return that a company is expected to pay to its shareholders to compensate them for the risk of investing in the equity of the company.

Leverage

The use of various financial instruments or borrowed capital, like debt, to increase the potential return of an investment.