Question 734414
Third Degree Polynomial:
{{{(x-a)(x-b)(x-c)}}}


A real zero is x=1:
{{{(x-1)(x-b)(x-c)}}}


x=1 is the only real zero, and multiplicity is 1:
{{{(x-1)(x-z[1])(x-z[2])}}},
where we want two complex numbers as conjugate pairs.  This part is open-ended.  For convenience we could pick 1-i and 1+i.

{{{(x-1)(x-(1-i))(x-(1+i))}}}
{{{(x-1)(x^2-(1-i)x-(1+i)x+(1-i)(1+i))}}}
{{{(x-1)(x^2-x+ix-x-ix+1+1)}}}
{{{highlight((x-1)(x^2-2x+2))}}}