Question 532226
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1.  *[tex \LARGE \ \ \ \ \ \ \ \ \ \ \rho_1(x)\ =\ (x\ -\ 1)(x\ -\ 4)(x\ +\ 3)]


All you have to do is multiply the binomials and collect like terms.


Do the others the same way, except remember that both complex and irrational zeros come in conjugate pairs, that is:


if


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ bi] is a zero


then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ -\ bi] must also be a zero


and if, where *[tex \Large \omega] is an algebraic irrational,


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ + b\omega] is a zero


then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a\ -\ b\omega] must also be a zero


Note:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2i\ =\ 0\ +\ 2i]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{2}\ =\ 0\ +\ \sqrt{2}]


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