Find All Complex Zeros of the Polynomial Function $$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39$$

question 34

Multiple Choice

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
- $$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 5 x + 39$$

• A) \(- 3,1 + 2 i , 1 - 2 i\)
• B) \(- 3,3 + 2 i , 3 - 2 i\)
• C) \(- 3,1 + 2 \sqrt { 13 } i , 1 - 2 \sqrt { 13 } i\)
• D) \(- 3,3 + 4 i , 3 - 4 i\)

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Definitions:

Vastus Lateralis

A muscle located on the side of the thigh, part of the quadriceps group, responsible for extending the knee.

Psoas Major

A large muscle in the human body that connects the lower spine to the upper thigh, crucial for hip flexion.

Rectus Femoris

A muscle in the quadriceps group that extends the knee and flexes the thigh at the hip.

Anterior Aspect

Referring to the front view or portion of a structure relative to the body's standard anatomical position.