For the Polynomial, List Each Real Zero and Its Multiplicity $$f ( x ) = 2 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } + 6 \right) ^ { 2 }$$

question 34

Multiple Choice

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at
each x -intercept.
- $$f ( x ) = 2 \left( x ^ { 2 } + 1 \right) \left( x ^ { 2 } + 6 \right) ^ { 2 }$$

• A) No real zeros
• B) \(- 1\), multiplicity 1 , touches \(x\)-axis; \(- 6\), multiplicity 2 , crosses \(x\)-axis
• C) 1 , multiplicity 1 , crosses \(x\)-axis; \(- 1\), multiplicity 1 , crosses \(x\)-axis; \(\sqrt { 6 }\), multiplicity 2 , touches \(x\)-axis; \(- \sqrt { 6 }\), multiplicity 2 , touches \(x\)-axis
• D) \(- 1\), multiplicity 1 , crosses \(x\)-axis; \(- 6\), multiplicity 2 , touches \(x\)-axis

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