Find All of the Real Zeros of the Function $$f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 2 x ^ { 2 } + 36 x - 48$$

question 259

Multiple Choice

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational.
- $$f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 2 x ^ { 2 } + 36 x - 48$$

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

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Definitions:

Absorption

The process by which substances are taken up and assimilated into the body, such as nutrients from the digestive tract into the bloodstream.

Mechanical Breakdown

The physical process of breaking food into smaller pieces, an essential part of digestion.

Chemical Digestion

The process of breaking down food in the gut into smaller components, using enzymes, so they can be absorbed into the body.

Common Hepatic Duct

A duct in the liver that conveys bile from the liver to the cystic duct and then to the gallbladder.