Find All Complex Zeros of the Polynomial Function $$f ( x ) = x ^ { 4 } - 9$$

question 272

Multiple Choice

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
- $$f ( x ) = x ^ { 4 } - 9$$

• A) \(\sqrt { 3 } , \sqrt { 3 } \mathrm { i }\)
• B) \(\sqrt { 3 } , - \sqrt { 3 }\)
• C) \(\sqrt { 3 } , - \sqrt { 3 } i , \sqrt { 3 } i , - \sqrt { 3 }\)
• D) \(\sqrt { 3 } , - \sqrt { 3 } , 3 \mathrm { i } , - 3 \mathrm { i }\)

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Definitions:

UV Spectra

The absorption or emission spectrum of a substance in the ultraviolet range, used to identify chemical bonding or concentration of a substance.

Electronic Transitions

Changes in the energy levels of electrons within atoms or molecules, which can result in absorption or emission of light at specific wavelengths.

Proton NMR Spectrum

A technique in nuclear magnetic resonance (NMR) that measures the environment of hydrogen atoms in a molecule to elucidate its structure.

Triplet

In chemistry, a term often used to describe a state of a molecule or an atom in which its electrons have a specific spin configuration leading to three closely related energy levels or quantum states.