Given that a polynomial with real coefficients has a root of , the other root must be .
Answer & Analysis
Analysis
Question Analysis
This problem tests the student's ability to apply the Conjugate Root Theorem to find the conjugate of a given complex root in a polynomial with real coefficients.
Key Concept Explanation
The Conjugate Root Theorem is essential for understanding the nature of roots in polynomials with real coefficients. It ensures 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 is
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