Find All Real Zeros of the Polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$

question 35

Multiple Choice

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$ and determine the mutiplicity of each.

• A) \(x = 0\), multiplicity \(2 ; x = - 2\), multiplicity \(1 ; x = - 6\), multiplicity 1
• B) \(x = 2\), multiplicity \(2 ; x = 6\), multiplicity 2
• C) \(x = 0\), multiplicity \(2 ; x = 2\), multiplicity \(1 ; x = 6\), multiplicity 1
• D) \(x = - 2\), multiplicity \(2 ; x = - 6\), multiplicity 2
• E) \(x = 0\), multiplicity \(1 ; x = 2\), multiplicity \(1 ; x = - 2\), multiplicity \(1 ; x = 6\), multiplicity 1

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Definitions:

Cell Metabolism

The complex set of life-sustaining chemical reactions in cells that allows organisms to grow, reproduce, maintain structures, and respond to environments.

Oxygen

A chemical element essential for most forms of life on Earth, used in cellular respiration.

Raw Materials

Basic materials from which products are made, including direct materials like wood for furniture or iron ore for steel production.

Isotonic Solution

Solution that is equal in solute concentration to that of the cytoplasm of a cell; causes cell to neither lose nor gain water by osmosis.