Find All of the Real Zeros of the Function $$f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 20 x - 32$$

question 67

Multiple Choice

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational.
- $$f ( x ) = x ^ { 3 } + 6 x ^ { 2 } - 20 x - 32$$

• A) \(- 8\) (rational), \(1 + \sqrt { 5 }\) (irrational), and \(1 - \sqrt { 5 }\) (irrational)
• B) \(- 8\) (rational), \(2 + \sqrt { 5 }\) (irrational), and \(2 - \sqrt { 5 }\) (irrational)
• C) \(- 8\) (rational), 6 (rational), \(- 4\) (rational)
• D) \(- 8\) (rational), \(\sqrt { 5 }\) (irrational), and \(- \sqrt { 5 }\) (irrational)

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Definitions:

Working Memories

A cognitive system that holds information temporarily available for processing tasks such as reasoning and comprehension.

Basal Ganglia

A group of structures linked to the thalamus in the base of the brain and involved in coordination of movement and behavior control.

Procedural Memories

Procedural memories are a type of long-term memory involved in the learning of motor skills and behaviors, allowing individuals to perform tasks without conscious awareness of the learned abilities.

Reticular Formation

A network of neurons in the brainstem involved in arousal and alertness.