Find All Solutions to the Following Equation $x ^ { 3 } + 729 = 0$

question 21

Multiple Choice

Find all solutions to the following equation. $x ^ { 3 } + 729 = 0$ ​

• A) \(x = - 9\)
• B) \(x = 9 i , - \frac { 9 \sqrt { 3 } } { 2 } - \frac { 9 } { 2 } i , \frac { 9 \sqrt { 3 } } { 2 } - \frac { 9 } { 2 } i\)
• C) \(x = - 9 i\)
• D) \(x = 9 i , - \frac { 9 \sqrt { 3 } } { 2 } - \frac { 9 } { 2 } i , - \frac { 9 \sqrt { 3 } } { 2 } + \frac { 9 } { 2 } i\)
• E) \(x = - 9 i , - \frac { 9 \sqrt { 3 } } { 2 } - \frac { 9 } { 2 } i , - \frac { 9 \sqrt { 3 } } { 2 } + \frac { 9 } { 2 } i\)

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Definitions:

Shortage Costs

Costs incurred by a business when the demand for its products exceeds its supply, often leading to lost sales and customer dissatisfaction.

Short-term Financial Policy

Guidelines or strategies focused on managing a company's current assets and liabilities to ensure short-term operational needs are met.

Carrying Costs

Expenses associated with holding inventory, including storage, insurance, and opportunity cost of tied-up capital.

Shortage Costs

Costs incurred from not having enough inventory on hand, including lost sales and emergency shipping expenses.