If the roots are $x = 3 ± 5i,$ then the factors must be $(x - (3 + 5i))$ and $(x - (3 - 5i))$.

Use the factors to write and simplify an equation.
$(x - 3 + 5i)(x - 3 - 5i) = 0$

$x^2 - 6x + 34 = 0$