Given that the roots of a polynomial are and , and the constant term is 6, the polynomial can be written as . Find the value of and the polynomial.
Answer & Analysis
Analysis
Question Analysis
This question assesses the ability to determine the leading coefficient and write the polynomial equation given the roots and a specific constant term.
Key Concept Explanation
The polynomial can be expressed as . By expanding and comparing the constant term, we can find the value of .
Step-by-step Solution
1. Identify the roots: and .
2. Write the factors: and .
3. Form the polynomial: .
4. Expand the expression:
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