Write the equation of a 4th degree polynomial function with the follo.pdf

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The document provides a solution to writing the equation of a 4th degree polynomial function with the roots x=1 with multiplicity 2, and x=i and x=-i. The polynomial function is (x-1)^2(x^2+1) as (x-1)^2 accounts for the repeated root of 1, and (x^2+1) accounts for the conjugate pair of roots i and -i.

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Write the equation of a 4th degree polynomial function with the following roots: x=1 with
multiplicity 2, and x i )
Solution
if one root is i other will be -i as conjugate pair
(x-i)(x+i) will be a factor
(x^2+1) will be a factor as i^2 =-1
another root is 1 with multiplicity 2
so the polynomial will be
(x-1)^2(x^2+1)
Thank you.

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