SOLUTION: Will you please help me write a quintic function with two imaginary roots, two irrational roots, and one rational root. Thanks!

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Question 838423: Will you please help me write a quintic function with two imaginary roots, two irrational roots, and one rational root. Thanks!

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x=sqrt(-1), x=-sqrt(sqrt(-1), x=sqrt(2), x=-sqrt(2), x=2
(x-sqrt(-1))*(x+sqrt(-1))=x^2+1
(x-sqrt(2))*(x+sqrt(2))=x^2-2
(x^2+1)(x^2-2)(x-2)
=x^5-2x^4-x^3+2x^2-2x+4
.
Ed