If [tex]p(3-2i)=0,[/tex] then complex number [tex]3-2i[/tex] is a root of cubic polynomial.
If polynomial has real coefficients, then conjugated [tex]3+2i[/tex] is also a root of polynomial.
Then the polynomial will be of a form
[tex]p(x)=(x-(3-2i))(x-(3+2i))(x-a).[/tex]
Since [tex]p(0)=-52,[/tex] then
[tex]-52=(0-(3-2i))(0-(3+2i))(0-a),\\ \\-52=(2i-3)(3+2i)a,\\ \\-52=(4i^2-9)a,\\ \\-52=(-4-9)a,\\ \\-13a=-52,\\ \\a=4.[/tex]
Therefore,
[tex]p(x)=(x-(3-2i))(x-(3+2i))(x-4),\\ \\p(x)=(x^2-6x+13)(x-4),\\ \\p(x)=x^3-10x^2+37x-52.[/tex]
