(i) .

Let

If given equation has four real and distinct roots, then both roots of (i) must be positive

[from (ii), (iii), (iv)]
(ii) If equation has no real roots, then (i) must have both roots negative for which

[from (ii), (iii), (v)]

Also for no real roots we can have

Hence,
(iii) From above discussion we have for equation has either four distinct real roots or no real roots.

For , both roots are

──────────────────────────────────────────────────────────────────────────────────────────