Find All Zeros of the Function and Write the Polynomial $$f ( x ) = x ^ { 4 } + 25 x ^ { 2 } + 144$$

question 243

Multiple Choice

Find all zeros of the function and write the polynomial as a product of linear factors.
- $$f ( x ) = x ^ { 4 } + 25 x ^ { 2 } + 144$$

• A) \(f ( x ) = ( x + 3 i ) ( x - 3 i ) ( x + 4 i ) ( x - 4 i )\)
• B) \(f ( x ) = ( x + i ) ( x - i ) ( x + 12 i ) ( x - 12 i )\)
• C) \(f ( x ) = ( x + 3 i ) ^ { 2 } ( x + 4 i ) ^ { 2 }\)
• D) \(f ( x ) = ( x + 3 + 4 i ) ^ { 2 } ( x + 3 - 4 i ) ^ { 2 }\)

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Definitions:

Hammond Postulate

A principle stating that the transition state of a chemical reaction resembles the structure of the closest stable species: the reactants for endothermic steps and the products for exothermic steps.

Free Radical Chlorine

A highly reactive species of chlorine that carries an unpaired electron, often involved in radical reactions.

Methane

A simple hydrocarbon with the formula CH4, representing the simplest alkane and a primary component of natural gas.

Regiochemistry

The study of the principles guiding the direction or position that new bonds form in a molecule during a chemical reaction.