A polynomial equation with roots and , and the constant term is -5, can be written as . Find the value of and the polynomial.
Answer & Analysis
Analysis
Question Analysis
This question tests the ability to determine the leading coefficient and write a second-degree polynomial equation from its roots and a given constant term, which is a fundamental skill in polynomial construction.
Key Concept Explanation
Given the roots and the constant term, the polynomial can be written as the product of the factors multiplied by a leading coefficient. The constant term helps determine the value of the leading coefficient.
Step-by-step Solution
1. Identify the roots: and .
2. Write the factors: and .
3. Multiply the factors by the leading coefficient: .
4. Expand the product:
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