Using the Given Zero, Find All Other Zeros of F(x) $3 i$

question 486

Multiple Choice

Using the given zero, find all other zeros of f(x) .
- $3 i$ is a zero of $f ( x ) = 16 x ^ { 4 } - 8 x ^ { 3 } + 154 x ^ { 2 } - 72 x + 90$

• A) \(- 3 \mathrm { i } , \frac { 1 } { 2 } + \frac { 3 } { 2 } \mathrm { i } , \frac { 1 } { 2 } - \frac { 3 } { 2 } \mathrm { i }\)
• B) \(- 3 \mathrm { i } , - \frac { 1 } { 4 } + \frac { \sqrt { 3 } } { 4 } \mathrm { i } , - \frac { 1 } { 4 } - \frac { \sqrt { 3 } } { 4 } \mathrm { i }\)
• C) \(- 3 \mathrm { i } , \frac { 1 } { 4 } + \frac { 3 } { 4 } \mathrm { i } , \frac { 1 } { 4 } - \frac { 3 } { 4 } \mathrm { i }\)
• D) \(- 3 \mathrm { i } , - \frac { 1 } { 2 } + \frac { 3 } { 2 } \mathrm { i } , - \frac { 1 } { 2 } - \frac { 3 } { 2 } \mathrm { i }\)

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Definitions:

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Membrane-bound Receptor

A type of receptor located on the cell membrane that binds to external molecules to initiate a cellular response.

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Bioactive lipid compounds derived from fatty acids, playing critical roles in inflammation, immunity, and as messengers in the central nervous system.

Prostaglandins

A group of lipid compounds that have diverse hormone-like effects, including mediating inflammation and pain.