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 2 years ago
Find the 3rd polynomial with roots 3 and 2 + i
I know my roots are 3, 2 + i, 2  i, but I don't know how to start my equation. Can someone please show me the steps to solve this problem?
 2 years ago
Find the 3rd polynomial with roots 3 and 2 + i I know my roots are 3, 2 + i, 2  i, but I don't know how to start my equation. Can someone please show me the steps to solve this problem?

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satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1you are looking for a quadratic whose zeros are \(2+i\) and \(2i\) when you find that, you need to multiply it by \(x3\) for your final answer there are a few ways to find the quadratic

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1one way is to memorize the following, if \(a+bi\) is a zero of a quadratic with leading coefficient 1, the quadratic is \[x^22ax+(a^2+b^2)\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1another way, in case you don't feel like memorizing that one, is to start with \[x=2+i\] and work backwards: \[x=2+i\] \[x2=i\] \[(x2)^2=i^2\] \[x^24x+4=1\] \[x^24x+5=0\]so your quadratic is \(x^24x+5\)

eunjii
 2 years ago
Best ResponseYou've already chosen the best response.0sorry I asked my question wrong. . .it was "Find the 3rd degree polynomial with roots 3 and 2 + i"

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1a final and not so pretty way is to start with \[(x(2+i))(x(2i))\] and multiply out

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1yes, that is what we are trying to do

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1first step, find the quadratic with zeros \(2+i\) and its conjugate \(2i\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1that will be \(x^24x+5\) no matter what method you use then your final answer will be \[(x3)(x^24x+5)\]

eunjii
 2 years ago
Best ResponseYou've already chosen the best response.0Thank you so much~<3 The explanation was very clear and helpful.
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