The value of
for which the equation
has both roots real, distinct and negative, is
Text Solution
Verified by Experts3
(3)
We have the quadratic:

For both roots to be real, distinct, and negative, we can also use Vieta's formulas:
Sum of roots: 
Since both roots are negative, 
Product of roots: 
Since both roots are negative,
(product of two negatives is positive)
So
(already satisfied for
)
Discriminant
: Already calculated

Now combine all conditions:
(sum negative)
(from discriminant)
Only integer value in this range is
.
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