Find All Zeros of the Function $f ( x ) = x ^ { 2 } ( x - 2 ) \left( x ^ { 3 } - 216 \right)$

question 75

Multiple Choice

Find all zeros of the function $f ( x ) = x ^ { 2 } ( x - 2 ) \left( x ^ { 3 } - 216 \right)$ .

• A) \(x = 2,216\)
• B) \(x = 0 , - 2 , - 6\)
• C) \(\quad x = 0,2,6 , - 3 - 3 \sqrt { 3 } i , - 3 + 3 \sqrt { 3 } i\)
• D) \(x = - 2 , - 216\)
• E) \(\quad x = 0,2,6\)

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Definitions:

Adenine

A purine base found in DNA and RNA, which pairs with thymine in DNA and with uracil in RNA during the formation of nucleic acids.

Nucleotide

A basic building block of DNA and RNA, consisting of a sugar, a phosphate group, and a nitrogenous base.

Nitrogen Base

A component of nucleotides in DNA and RNA, which includes adenine, thymine (in DNA), uracil (in RNA), guanine, and cytosine.

Uracil

A nitrogen-containing base found in RNA, where it pairs with adenine and replaces thymine during DNA transcription.