Find All Rational, Irrational, and Complex Zeros $P ( x ) = x ^ { 4 } + x ^ { 3 } - 5 x ^ { 2 } - 3 x + 6$

question 22

Multiple Choice

Find all rational, irrational, and complex zeros. $P ( x ) = x ^ { 4 } + x ^ { 3 } - 5 x ^ { 2 } - 3 x + 6$

• A) \(\{ - 3,3,1 , - 2 \}\)
• B) \(\{ - 3,1 , - 2 \}\)
• C) \(\{ - \sqrt { 3 } , \sqrt { 3 } , 1 , - \sqrt { 2 } \}\)
• D) \(\{ - \sqrt { 3 } , \sqrt { 3 } , 1 , - 2 \}\)
• E) \(\{ \sqrt { 3 } , - 6 \}\)

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Definitions:

Dimethyldodecane

An organic compound structured as a dodecane backbone with two methyl groups attached, used in various chemical contexts.

Alkane

A hydrocarbon compound consisting only of carbon and hydrogen atoms arranged in a tree structure with single bonds.

Alkane

Saturated hydrocarbons consisting of carbon and hydrogen atoms connected by single bonds in a tree structure, without any cycles or double bonds.

IUPAC Name

The systematic name of a chemical substance as determined by the rules of the International Union of Pure and Applied Chemistry.