Question 735303: How can I find the fourth-degree polynomial with interger coefficients that have 3i and sqrt of 6. Along with 2+i and 1- sqrt of 5
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The first thing to do is to recognize that there are no such things as intergers. It is possible to have a polynomial with integer coefficients, so I'll assume that is what you mean. Next, if I assume that you followed the fairly easy to comprehend instructions for posting, in particular the rule that says "One question per post", then I have to assume that the four roots that you gave are four roots of the same 4th degree polynomial. Given that, there is no answer to your question. If you have integer coefficients, then both complex and irrational zeros must come in conjugate pairs. Given the four numbers you supplied, that would imply that your 4th degree polynomial has eight zeros; impossible according to the Fundamental Theorem of Algebra.
On the other hand, if you were actually asking two different questions in the same post, I would insist that the very first lesson you learn here is that the ability to read, comprehend, and follow written instructions is one of the most basic of necessary math skills without which you are doomed to failure as a mathematics student.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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