Given the roots of a polynomial equation are and , and the constant term is 42, the polynomial can be written as . Find the value of and the polynomial.
Answer & Analysis
Analysis
Question Analysis
This question requires students to find the coefficient of a polynomial given its roots and the constant term. It tests the understanding of how to use the constant term to determine the leading coefficient.
Key Concept Explanation
The constant term of a polynomial is the term without the variable. In the expanded form, it is the product of the constant terms in the factored form. For example, if the roots are and , and the constant term is 42, the polynomial can be written as .
Step-by-step Solution
1. Start with the given roots: and .
2. Write the polynomial as .
3. Expand the expression:
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