Find a Polynomial Function of the Lowest Degree with Real $0,2,4 - i$

question 54

Multiple Choice

Find a polynomial function of the lowest degree with real coefficients that has the zeros below and whose leading coefficient is one.
$0,2,4 - i$

• A) \(f ( x ) = x ^ { 4 } - 34 x ^ { 3 } + 32 x ^ { 2 } - 10 x\)
• B) \(f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 33 x ^ { 2 } - 34 x\)
• C) \(f ( x ) = x ^ { 4 } + 32 x ^ { 3 } - 10 x ^ { 2 } - 34 x\)
• D) \(f ( x ) = x ^ { 4 } - 10 x ^ { 3 } - 34 x ^ { 2 } + 32 x\)
• E) \(f ( x ) = x ^ { 4 } + 32 x ^ { 3 } - 34 x ^ { 2 } - 10 x\)

---

Definitions:

Parsimonious

Referring to the principle in science and philosophy where the simplest explanation or strategy tends to be the right one.

Replicable

The ability of a study or experiment to be repeated and yield the same results.

Falsifiable

A criterion of the scientific method stating that for a proposition to be considered scientifically valid, it must be possible to conceive an observation that could prove the proposition false.

Psychoanalytic

Pertaining to a therapeutic and theoretical approach originated by Sigmund Freud that emphasizes unconscious motivations and conflicts in understanding human behavior.