Find the Zeros for the Polynomial Function and Give the Multiplicity

question 32

Multiple Choice

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the
x-axis or touches the x-axis and turns around, at each zero.
- $$f ( x ) = \frac { 1 } { 3 } x ^ { 4 } \left( x ^ { 2 } - 3 \right) ( x + 8 )$$

• A) 0 , multiplicity 4 , touches \(x\)-axis and turns around;
• \(- 8\), multiplicity 1 , crosses \(x\)-axis
• 3 , multiplicity 2 , touches \(x\)-axis and turns around
• B) 0 , multiplicity 4 , touches \(x\)-axis and turns around;
• \(- 8\), multiplicity 1 , crosses \(x\)-axis;
• \(\sqrt { 3 }\), multiplicity 1 , crosses \(x\)-axis;
• \(- \sqrt { 3 }\), multiplicity 1 , crosses \(x\)-axis
• C) 0 , multiplicity 4 , crosses \(x\)-axis;
• \(- 8\), multiplicity 1 , touches \(x\)-axis and turns around;
• \(\sqrt { 3 }\), multiplicity 1 , touches \(x\)-axis and turns around;
• \(- \sqrt { 3 }\), multiplicity 1 , touches \(x\)-axis and turns around
• D) 0 , multiplicity 4 , touches \(x\)-axis and turns around; \(- 8\), multiplicity 1 , crosses \(x\)-axis

Comprehend the structure and implications of centralized and decentralized business organizations.

Recognize the role and impact of budgets and budget performance reports in managing responsibility centers.

Identify the characteristics and responsibilities of different types of responsibility centers.

Understand the process and significance of responsibility accounting in organizational management.

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Definitions:

Least Cost

A principle or strategy focused on achieving a particular objective at the minimum possible cost.

Short Run

A period in economics where at least one factor of production is fixed, and firms can only partially adjust to changes in market demand.

Input

Resources such as labor, materials, and capital used in the production of goods and services.

Planned Output

The quantity of goods or services that a company intends to produce in a specific period.