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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