Find All of the Real Zeros of the Function $$f ( x ) = x ^ { 4 } + 2 x ^ { 3 } - 17 x ^ { 2 } - 4 x + 30$$

question 365

Multiple Choice

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational.
- $$f ( x ) = x ^ { 4 } + 2 x ^ { 3 } - 17 x ^ { 2 } - 4 x + 30$$

• A) \(- 5\) (rational), 3 (rational), \(2 + \sqrt { 2 }\) (irrational), and \(2 - \sqrt { 2 }\) (irrational)
• B) 5 (rational), \(- 3\) (rational), \(\sqrt { 2 }\) (irrational), and \(- \sqrt { 2 }\) (irrational)
• C) \(- 5\) (rational), 3 (rational), \(\sqrt { 2 }\) (irrational), and \(- \sqrt { 2 }\) (irrational)
• D) 5 (rational), \(- 3\) (rational), \(2 + \sqrt { 2 }\) (irrational), and \(2 - \sqrt { 2 }\) (irrational)

---

Definitions:

Administrative Costs

Expenses related to the general operations of a business that are not directly tied to the production of goods or services.

Direct Material

Raw materials that can be directly traced to the production of a specific product.

Product Costs

Costs that are considered to be directly associated with the production of goods or services, including direct labor, direct materials, and manufacturing overhead.

Depreciation

The allocation of the cost of tangible assets over their useful lives, reflecting the decrease in value due to wear and tear, age, or obsolescence.