anonymous
  • anonymous
Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree: 4; zeros: 2i and -3i
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
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.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
KingGeorge
  • KingGeorge
In general, if you have a polynomial with real coefficients, and some complex root \(\alpha i\) where \(\alpha\) is a real number, the you also have the complex root \(-\alpha i\). Using this, can you tell me what all the roots of your polynomial will be?
anonymous
  • anonymous
2i, -2i, -3i, and 3i?
KingGeorge
  • KingGeorge
Bingo. So that means your factored polynomial will be \[(x-2i)(x+2i)(x-3i)(x+3i).\]Now you just have to expand it out.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
i got this answer: x^3 -3ix^2-2ix^2+6ix^2-4xi^2+12i^2.
KingGeorge
  • KingGeorge
Hmmm. I've definitely got something different. I'll walk you through the first few steps I did. \[(x-2i)(x+2i)=x^2-2ix+2ix-(2i)^2=x^2-4(-1)=x^2+4\]Note that \(i^2=-1\) by definition. Similarly, \[(x-3i)(x+3i)=x^2-3ix+3ix-(3i)^2=x^2-9(-1)=x^2+9\]Using this, can you find \[(x^2+4)(x^2+9)\]on your own?

Looking for something else?

Not the answer you are looking for? Search for more explanations.