Question 193367
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The answer to that question really depends on what you think (or more to the point what your instructor thinks) is simpler, a 3rd degree polynomial function with irrational coefficients or a 4th degree polynomial function with integer coefficients.


Perform the indicated multiplications


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(x - \sqrt{5}\right)\left(x - (7 + i)\right)\left(x - (7 - i)\right)]


to obtain the 3rd degree polynomial.  You should end up with irrational coefficients on the constant, 1st, and 2nd degree terms.


Perform the indicated multiplications


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(x - \sqrt{5}\right)\left(x + \sqrt{5}\right)\left(x - (7 + i)\right)\left(x - (7 - i)\right)]


to obtain the 4th degree polynomial with integer coefficients.


<b>Update:</b>


It just occurred to me that you could multiply:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(x - \sqrt{5}\right)\left(x - (7 + i)\right)]


to obtain a 2nd degree polynomial with complex coefficients.


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