## anonymous one year ago Write a polynomial of the smallest degree with roots -8, 9, 10, and -11.

1. SolomonZelman

The smallest polynomial with roots: $$\large\color{black}{ \displaystyle \color{blueviolet}{\rm a}, \color{blue}{~\rm b},\color{brown}{~\rm c},\color{green}{~\rm d} }$$ $$\large\color{black}{ \displaystyle f(x)=(x-\color{blueviolet}{\rm a})(x-\color{blue}{\rm b})(x-\color{brown}{\rm c})(x-\color{green}{\rm d}) }$$

2. SolomonZelman

This is also true with more roots or less roots. For example, below: The smallest polynomial with roots: $$\large\color{black}{ \displaystyle \color{blueviolet}{\rm a}, \color{blue}{~\rm b},\color{brown}{~\rm c},\color{green}{~\rm d},\color{darkgoldenrod}{~\rm k},\color{magenta}{~\rm l} }$$ $$\large\color{black}{ \displaystyle f(x)=(x-\color{blueviolet}{\rm a})(x-\color{blue}{\rm b})(x-\color{brown}{\rm c})(x-\color{green}{\rm d})(x-\color{darkgoldenrod}{\rm k})(x-\color{magenta}{\rm l}) }$$

3. SolomonZelman

Should I give you an example with numbers?

4. anonymous

No, I think I get it now. Thanks

5. SolomonZelman

Ok, do you want to post your answer for me to make sure it is correct?

6. anonymous

Sure, I am getting x^4-183x^2+38x+7920 as my answer

7. SolomonZelman

* Yes, that is exactly right! *

8. anonymous

Cool!! thanks!

9. SolomonZelman

You welcome!