Polynomial functions: form degree-3 poly w/ real coeff's and 8+i, -5 are roots

[Markymarcusdc]

Form a degree-3 polynomial with real coefficients such that 8 + i and -5 are roots.

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I have also attached the problem and text in a photo document to the post.

 

[ksdhart2]

That sure is a very nice homework problem you've got there. But, now you need to re-read the Read Before Posting!! thread that's stickied at the top of each sub-forum. What are your thoughts? What have you tried? Please share with us any and all work you've done on this problem, even the parts you know for sure are wrong. The more specific you can be about what you've already done and exactly where things are getting bogged down, the better quality help we can provide. Thank you.

(P.S. Assuming you're stuck at the very beginning and thus have no work to show, a great place to begin is to review the factor theoremhttps://www.mathsisfun.com/algebra/polynomials-remainder-factor.html and think about how that applies here)

 

[Steven G]

Form a degree-3 polynomial with real coefficients such that 8 + i and -5 are roots.

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I have also attached the problem and text in a photo document to the post.

Hint: If c is a root, then x-c is a factor. Also if a+bi is a root (b not 0), then a-bi is a root as well. So the cubic will be(x-c)(x-(a+bi))(x-(a-bi)) = (x-c)(x-a-bi)(x-a+bi) = (x-c)((x-a)-bi)((x-a)+bi). Believe it or not but this is a very big hint.