Find All Solutions of the Equation $$x ^ { 5 } - 243 = 0$$

question 286

Multiple Choice

Find all solutions of the equation. Leave answers in trigonometric form.
- $$x ^ { 5 } - 243 = 0$$

• A) \(\{ 3 , - 3 \}\)
• B) \(\left\{ 3 \operatorname { cis } 0,3 \operatorname { cis } \frac { 2 \pi } { 5 } , 3 \operatorname { cis } \frac { 4 \pi } { 5 } , 3 \operatorname { cis } \frac { 6 \pi } { 5 } , 3 \operatorname { cis } \frac { 8 \pi } { 5 } \right\}\)
• C) \(\left\{ 243 \operatorname { cis } 0,243 \operatorname { cis } \frac { 2 \pi } { 5 } , 243 \operatorname { cis } \frac { 4 \pi } { 5 } , 243 \operatorname { cis } \frac { 6 \pi } { 5 } , 243 \operatorname { cis } \frac { 8 \pi } { 5 } \right\}\)
• D) \(\left\{ 3 \operatorname { cis } \frac { \pi } { 5 } , 3 \operatorname { cis } \frac { 3 \pi } { 5 } , 3 \right.\) cis \(\pi , 3\) cis \(\frac { 7 \pi } { 5 } , 3\) cis \(\left. \frac { 9 \pi } { 5 } \right\}\)

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Definitions:

Confidence Interval

A range of values derived from sample statistics that is likely to cover the true parameter of the population with a certain level of confidence.

Standard Deviation

A statistic that measures the dispersion of a dataset relative to its mean.

T-Distribution

A probability distribution used in statistics for estimating population parameters when the sample size is small and the population variance is unknown.

Confidence Intervals

A range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter, expressed with a certain level of confidence.