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)

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