anonymous
  • anonymous
Write a polynomial of the smallest degree with roots -8, 9, 10, and -11.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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SolomonZelman
  • SolomonZelman
The smallest polynomial with roots: \(\large\color{black}{ \displaystyle \color{blueviolet}{\rm a}, \color{blue}{~\rm b},\color{brown}{~\rm c},\color{green}{~\rm d} }\) \(\large\color{black}{ \displaystyle f(x)=(x-\color{blueviolet}{\rm a})(x-\color{blue}{\rm b})(x-\color{brown}{\rm c})(x-\color{green}{\rm d}) }\)
SolomonZelman
  • SolomonZelman
This is also true with more roots or less roots. For example, below: The smallest polynomial with roots: \(\large\color{black}{ \displaystyle \color{blueviolet}{\rm a}, \color{blue}{~\rm b},\color{brown}{~\rm c},\color{green}{~\rm d},\color{darkgoldenrod}{~\rm k},\color{magenta}{~\rm l} }\) \(\large\color{black}{ \displaystyle f(x)=(x-\color{blueviolet}{\rm a})(x-\color{blue}{\rm b})(x-\color{brown}{\rm c})(x-\color{green}{\rm d})(x-\color{darkgoldenrod}{\rm k})(x-\color{magenta}{\rm l}) }\)
SolomonZelman
  • SolomonZelman
Should I give you an example with numbers?

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anonymous
  • anonymous
No, I think I get it now. Thanks
SolomonZelman
  • SolomonZelman
Ok, do you want to post your answer for me to make sure it is correct?
anonymous
  • anonymous
Sure, I am getting x^4-183x^2+38x+7920 as my answer
SolomonZelman
  • SolomonZelman
* Yes, that is exactly right! *
anonymous
  • anonymous
Cool!! thanks!
SolomonZelman
  • SolomonZelman
You welcome!

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