Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

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?

I got my questions answered at in under 10 minutes. Go to now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly


Get your free account and access expert answers to this and thousands of other questions

you are looking for a quadratic whose zeros are \(2+i\) and \(2-i\) when you find that, you need to multiply it by \(x-3\) for your final answer there are a few ways to find the quadratic
one way is to memorize the following, if \(a+bi\) is a zero of a quadratic with leading coefficient 1, the quadratic is \[x^2-2ax+(a^2+b^2)\]
another way, in case you don't feel like memorizing that one, is to start with \[x=2+i\] and work backwards: \[x=2+i\] \[x-2=i\] \[(x-2)^2=i^2\] \[x^2-4x+4=-1\] \[x^2-4x+5=0\]so your quadratic is \(x^2-4x+5\)

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

sorry I asked my question wrong. . .it was "Find the 3rd degree polynomial with roots 3 and 2 + i"
a final and not so pretty way is to start with \[(x-(2+i))(x-(2-i))\] and multiply out
yes, that is what we are trying to do
first step, find the quadratic with zeros \(2+i\) and its conjugate \(2-i\)
that will be \(x^2-4x+5\) no matter what method you use then your final answer will be \[(x-3)(x^2-4x+5)\]
Thank you so much~<3 The explanation was very clear and helpful.

Not the answer you are looking for?

Search for more explanations.

Ask your own question