Find All Rational, Irrational, and Complex Zeros (And State Their $p ( x ) = x ^ { 3 } - x ^ { 2 } - 2 x + 2$

question 63

Multiple Choice

Find all rational, irrational, and complex zeros (and state their multiplicities) . $p ( x ) = x ^ { 3 } - x ^ { 2 } - 2 x + 2$

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

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Definitions:

Sense of Isolation

The feeling of being detached or separated from others, often leading to loneliness or depression.

Sense of Despair

A profound feeling of hopelessness and inadequacy, often associated with existential crises or the late stages of Erikson's psychosocial development theory.

Feelings of Generativity

A sense of contribution to the well-being of the next generation, characterized by a desire to nurture, guide, and offer outputs to society that lasts beyond one's lifetime.

Wisdom and Integrity

Wisdom refers to the quality of having deep knowledge, insight, or judgement, while integrity involves adherence to moral and ethical principles, signifying honesty and trustworthiness.