SOLUTION: Can you please help me solve this question? Write a polynomial equation of the least degree with the roots 4,1,i,and -1.

Question 165853: Can you please help me solve this question? Write a polynomial equation of the least degree with the roots 4,1,i,and -1.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write a polynomial equation of the least degree with the roots 4,1,i,and -1.
:
Write factors from the roots
(x-4)
(x+1)*(x-1) = (x^2 - 1) = 0
and
x = i
x^2 = i^2
x^2 = -1
(x^2+1) = 0
:
(x^2-1) * (x^2+1) = x^4 -x^2 + x^2 - 1 = x^4 - 1
then
(x-4)*(x^4-1) = x^5 - x - x^4 + 4
:
Arrange to: x^5 - 4x^4 - x + 4
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