A polynomial equation has roots , , and . If the coefficient of the first-degree term is 1, write the third-degree polynomial equation in standard form. The equation is ________.
Answer & Analysis
Analysis
Question Analysis
This question tests the ability to write a polynomial equation from its roots and a given coefficient, which involves both factorization and algebraic manipulation.
Key Concept Explanation
If the roots of a polynomial equation are known, the equation can be written as the product of factors. The coefficient of a specific term can be used to determine the leading coefficient.
Step-by-step Solution
1. Identify the roots: , , and .
2. Write the factors: , , and .
3. Form the initial equation: .
4. Expand the factors: .
5. Multiply by the leading coefficient
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