(i) , (ii) , (iii) .

Let (purely imaginary) be a root of the given equation. Then,

and ……… (i)

……… . (ii)

Now Eqs. (i) and (ii) must have one common root.
Let and be two purely imaginary roots. Then,

……… .. (iii)

…………… . (iv)

Equations (iii) and (iv) must be identical as their roots are same.

Hence, is purely real and and are purely imaginary.
Let (purely real) be a root of the given equation. Then,

…………… (v)

and
or
or
or ……………… (vi)

Now (v) and (vi) must have one common root. Hence,

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