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

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Definitions:

Compounded Annually

The process where interest is calculated once per year and added to the principal, affecting future interest calculations.

Trust Fund

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Rate Of Return

A measure of the profit or loss of an investment over a given period, typically expressed as a percentage of the investment's initial cost.

Average Rate Of Return

The mean annual growth rate of an investment over a specified period of time, expressed as a percentage.