Question 342611
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If *[tex \Large \alpha] is a root of a polynomial equation, then *[tex \Large x\ -\ \alpha] must be a factor of the polynomial.  Since a quadratic equation has two roots, if you are given both of them, you can immediately derive the two factors of the quadratic trinomial:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ -\ \sqrt{2}\right)\left(x\ -\ 5\sqrt{2}\right)]


Just multiply the two binomials using FOIL.  Note:  Not all of the coefficients of your final answer will be rational.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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