Write the equation of a 4th degree polynomial function with

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.