Math Problem Statement
Solution
To determine the additional roots of the polynomial with rational coefficients:
Key Concept:
If a polynomial has rational coefficients and contains irrational roots like or , their conjugates and must also be roots of the polynomial.
Given Roots:
Additional Roots:
Their conjugates are:
Correct Answer:
The correct option is:
Let me know if you'd like a detailed explanation or further assistance.
5 Related Questions:
- How are conjugate roots determined for polynomials with rational coefficients?
- Why must irrational roots occur in conjugate pairs in these cases?
- Can a polynomial have one irrational root without its conjugate?
- What are examples of polynomials where roots include complex numbers?
- How does the degree of a polynomial relate to its number of roots?
Tip: Always ensure the polynomial's coefficients are rational before assuming conjugate roots must exist.
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Math Problem Analysis
Mathematical Concepts
Polynomial equations
Conjugate roots
Rational coefficients
Formulas
-
Theorems
Conjugate root theorem
Suitable Grade Level
Grades 10-12
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