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 351

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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Definitions:

Malthusian Theory

A theory proposed by Thomas Malthus suggesting that population growth will outpace agricultural production and lead to widespread poverty and famine.

Geometric Progression

A sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Arithmetic Progression

A sequence of numbers in which each term after the first is obtained by adding a constant, known as the common difference, to the preceding term.

Output Per Head

The average production of goods and services per individual in a specific period, typically used to measure labor productivity.