Find All Solutions to the Following Equation $$x ^ { 3 } - 216 = 0$$

question 102

Multiple Choice

Find all solutions to the following equation.
$$x ^ { 3 } - 216 = 0$$

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

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Definitions:

Operant

Pertaining to operant conditioning, a method of learning that employs rewards and punishments for behavior, leading to changes in that behavior's frequency.

Systematic Desensitization

A therapeutic intervention aimed at reducing an individual's anxiety responses through gradual exposure to the feared object or situation, along with relaxation techniques.

Relaxation Training

A therapeutic technique designed to help individuals learn to reduce stress and anxiety through specific physical exercises and controlled breathing.

Assertiveness Training

A behavioral therapy technique designed to help individuals clearly and confidently express their needs and rights without infringing on the rights of others.