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Write a polynomial of least degree with real coefficients and with the root . Write your answer using the variable and in standard form with a leading coefficient of .
Full solution
Q. Write a polynomial of least degree with real coefficients and with the root . Write your answer using the variable and in standard form with a leading coefficient of .
- Identify conjugate complex root: Identify the conjugate of the given complex root , which is .
- Write corresponding factors: Write the factors corresponding to these roots: and .
- Expand the factors: Expand the factors: .
- Apply difference of squares: Apply the difference of squares formula: .
- Simplify the expression: Simplify the expression: .
- Replace with : Since , replace with : .
- Expand : Expand : .
- Combine like terms: Combine like terms: .
