Use the Intermediate Value Theorem to Determine Whether the Polynomial $f ( x ) = 9 x ^ { 5 } + 6 x ^ { 3 } - 4 x ^ { 2 } + 1$

question 139

Multiple Choice

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the
given integers.
- $f ( x ) = 9 x ^ { 5 } + 6 x ^ { 3 } - 4 x ^ { 2 } + 1$ ; between $- 1$ and 0

• A) \(f ( - 1 ) = - 18\) and \(f ( 0 ) = 1\); yes
• B) \(\mathrm { f } ( - 1 ) = 18\) and \(\mathrm { f } ( 0 ) = 1\); no
• C) \(f ( - 1 ) = - 18\) and \(f ( 0 ) = - 1\); no
• D) \(f ( - 1 ) = 18\) and \(f ( 0 ) = - 1\); yes

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Definitions:

Population Proportion

The fraction or percentage of a population that exhibits a particular trait or characteristic.

Confidence Interval

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

Population Proportion

The fraction of the population that possesses a particular attribute, characteristic, or trait.

Standard Normal Distribution

A probability distribution that has a mean of zero and a standard deviation of one, used in statistical analysis to represent standardized values of a dataset.