The two roots given need counterparts so that the polynomial coefficients are real.
The counterparts are 11+2i and 8-13i.
The polynomial becomes p(x)=a(x^2-22x+121+4)(x^2-16x+64+169)=a(x^2-22x+125)(x^2-16x+233).
(This is the result of a((x-11-2i)(x-11+2i)(x-8+13i)(x-8-13i)).)
p(x)=a(x^4-38x^3+710x^2-7126x+29125), where a is a real number.