Given that one root of a polynomial with real coefficients is , the other root must be .
Answer & Analysis
Analysis
Question Analysis
This problem assesses the student's ability to apply the Conjugate Root Theorem to identify the conjugate of a given complex root.
Key Concept Explanation
The Conjugate Root Theorem is crucial for understanding the nature of roots in polynomials with real coefficients. It guarantees that if a complex number is a root, its conjugate must also be a root.
Step-by-step Solution
1. Identify the given root:
2. Apply the Conjugate Root Theorem: The conjugate of
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