(i) Let .

has at least one positive solution, then either both the roots of equation are non-negative or 0 lies between the roots.

Now sum of roots ; hence, case I is not possible. For case II,

(ii)

If has at least one negative solution, then either both the roots of equation are non-positive or 0 lies between the roots.

For case I , sum of roots is . Product of roots is

and

Hence, .

For case II,

(iii) If is true , then and .

and

and

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