Given that a polynomial with real coefficients has a root of , the other root must be .
Answer & Analysis
Analysis
Question Analysis
This problem evaluates the student's understanding of the Conjugate Root Theorem, which states that if a polynomial with real coefficients has a complex root, then its conjugate is also a root.
Key Concept Explanation
The Conjugate Root Theorem ensures that for any polynomial with real coefficients, if is a root, then is also a root. This is because the coefficients are real, and the polynomial must remain balanced in the complex plane.
Step-by-step Solution
1. Identify the given root: .
2. Apply the Conjugate Root Theorem: The conjugate of
Click "Show Answer" to reveal the answer and analysis
Want More Practice Questions?
Access thousands of practice questions with detailed explanations on Scholardog.