Use Descartes' Rule of Signs and the Rational Zeros Theorem $$f ( x ) = 4 x ^ { 3 } + 19 x ^ { 2 } - 8 x + 15$$

question 61

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.
- $$f ( x ) = 4 x ^ { 3 } + 19 x ^ { 2 } - 8 x + 15$$

• A) \(1 , \frac { 4 } { 3 } , - 5 ; f ( x ) = ( 4 x - 3 ) ( x - 1 ) ( x + 5 )\)
• B) \(- 5 , \frac { 3 } { 4 } , 1 ; f ( x ) = ( 4 x - 3 ) ( x - 1 ) ( x + 5 )\)
• C) \(- 1 , \frac { 4 } { 3 } , - 5 ; f ( x ) = ( 4 x - 3 ) ( x - 5 ) ( x + 1 )\)
• D) \(- 1 , \frac { 3 } { 4 } , 5 ; f ( x ) = ( 4 x - 3 ) ( x - 5 ) ( x + 1 )\)

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Definitions:

Worse Off

A situation in which an individual, group, or economy is in a poorer or less advantageous position compared to a previous state or another entity.

Equitable

Characterized by fairness and impartiality; ensuring just treatment or distribution of resources without favoritism or discrimination.

Externalities

Economic side effects or by-products that affect an uninvolved third party; can be either positive or negative.

Pareto Efficient

A circumstance in resource distribution where any improvement for one individual means a disadvantage for at least another.