Use the Intermediate Value Theorem to Determine Whether the Polynomial $$f ( x ) = 5 x ^ { 3 } - 7 x ^ { 2 } + 4 x - 7 ; [ 1,2 ]$$

question 184

Multiple Choice

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.
- $$f ( x ) = 5 x ^ { 3 } - 7 x ^ { 2 } + 4 x - 7 ; [ 1,2 ]$$

• A) \(f ( 1 ) = - 5\) and \(f ( 2 ) = 13\); yes
• B) \(f ( 1 ) = 5\) and \(f ( 2 ) = - 13\); yes
• C) \(f ( 1 ) = 5\) and \(f ( 2 ) = 13\); no
• D) \(f ( 1 ) = - 5\) and \(f ( 2 ) = - 13\); no

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Definitions:

Means

The average of a set of numbers, calculated by dividing the sum of all the values by the count of the values.

Equal-variances Test

A statistical test used to check if two populations have equal variances.

Student T-distributed

The Student's t-distribution is a probability distribution that is symmetric and bell-shaped, used especially in small sample sizes for estimating population parameters.

Degrees Of Freedom

The quantity of distinct values or parameters that can be allocated to a statistical test or distribution while adhering to all restrictions.