Question

A monic polynimial of degree 5 in ℝ[x] has 2 as a root of multiplicity 3
and 3 + i as a root of multiplicity 1. Write it as a product of first-degree factors in ℂ[x], then as a product of factors in ℝ[x].

Answer 1

the roots of the equation are 2,2,2,3+i,3-i (As complex roots occur in pairs) So the factors would be (x-2)^3 * (x-3-i)*(x-3+i) ... Which can further be simplified as (x-2)^3 * ((x-3)^2+1) ....