Find a Polynomial $P$ Of Degree $5$ , with Integer Coefficients, That Has Zeros Of

question 136

Essay

Find a polynomial $P$ of degree $5$ , with integer coefficients, that has zeros of $i$ and $2$ , with $i$ being a zero of multiplicity $2$ , and $P$ having a leading coefficient of $2$ .

---

Definitions:

Coupled Reaction

A coupled reaction is a chemical reaction where an energetically unfavorable reaction is driven by an energetically favorable one, often involving the transfer of electrons or energy.

Endergonic Reaction

Chemical reaction that requires an input of energy; opposite of exergonic reaction.

Exergonic Reaction

An exergonic reaction is a chemical reaction where energy is released, typically in the form of heat, making the reaction spontaneous.

Pyruvate

A key intermediate in several metabolic pathways, including glycolysis, linking the metabolism of carbohydrates, proteins, and fats.