Determine the Real Zeros of the Polynomial and Their Multiplicities $$f ( x ) = 3 ( x - 2 ) ( x - 6 ) ^ { 4 }$$

question 39

Multiple Choice

Determine the real zeros of the polynomial and their multiplicities. Then decide whether the graph touches or crosses the
x-axis at each zero.

- $$f ( x ) = 3 ( x - 2 ) ( x - 6 ) ^ { 4 }$$

• A)-2, multiplicity 1, touches x-axis; -6, multiplicity 4, crosses x-axis
• B)2, multiplicity 1, touches x-axis; 6, multiplicity 4, crosses x-axis
• C)-2, multiplicity 1, crosses x-axis; -6, multiplicity 4, touches x-axis
• D)2, multiplicity 1, crosses x-axis; 6, multiplicity 4, touches x-axis

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Definitions:

Randomized Block

A design of experiment that aims to reduce variation from confounding variables by grouping them into blocks before randomly applying treatments within each block.

Analysis of Variance

A statistical method used to test the differences between two or more means by analyzing variance.

Matched Pairs

refers to a design in experiments where each case has a unique counterpart for comparison, minimizing variability.

Interval

A range of numbers between two set points, often used in mathematics and statistics to specify subsets of the real number line.