Question 197839
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If a quadratic equation has roots *[tex \LARGE a] and *[tex \LARGE b], then *[tex \LARGE x - a] and *[tex \LARGE x - b] are factors of the quadratic polynomial, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(x - (3 + i)\right)\left(x - (3 - i)\right)]


are the factors of the polynomial that you are looking for.  Just multiply it out and collect like terms to find the appropriate quadratic polynomial.  Hint:  Consider 3 + i and 3 - i as single numbers and use FOIL.  The product of those two numbers will be the difference of two squares.  Also remember that *[tex \LARGE i^2 = -1]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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