To find the set of all values of for which both roots of the equation
are negative real numbers, follow these steps:

Discriminant Condition:
The equation's discriminant must be nonnegative for real roots:

Simplifying this:

This can be factored as:

Meaning …… . (i)

Sum of Roots Condition:

The sum of the roots (which is ) must be negative:

… . (ii)

Product of Roots Condition:

The product of the roots must be positive:

…… . (iii)

Determine the Valid Interval:

Combine the results from conditions (i), (ii), and (iii). From conditions (i) and (ii), we find :

Intersection of and gives:

Calculate :

With and , compute:

Therefore, the difference is 5.

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