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

Use the factors to write an equation.
(x − 3 + 5i)(x − 3 − 5i) = 0

Multiply.
(x − 3)² − 25i ² = 0

x² − 6x + 34 = 0