Given equation is x^{2} + 3ix + 10 = 0

Comparing with ax^{2} + bx + c = 0, we get

a = 1, b = 3i, c = 10

Discriminant = b^{2} – 4ac

= (3i)^{2} – 4 × 1 × 10

= 9i^{2} – 40

= -9 – 40 ……[∵ i^{2} = -1]

= -49 < 0

So, the given equation has complex roots.

These roots are given by

∴ x = 2i or x = -5i

∴ The roots of the given equation are 2i and -5i.