Mark the Correct alternative in the following:
The set of all vales of m for which both the roots of the equation are real and negative, is
For roots to be real its D ≥ 0
(m + 1)2 – 4(m + 4) ≥ 0
m2 – 2m – 15 ≥ 0
(m – 1)2 – 16 ≥ 0
(m – 1)2 ≥ 16
m – 1 ≤ -4 or m – 1 ≥ 4
m ≤ -3 or m ≥ 5
For both roots to be negative product of roots should be
positive and sum of roots should be negative.
Product of roots = m + 4 > 0 ⇒ m > -4
Sum of roots = m + 1 < 0 ⇒ m < -1
After taking intersection of D ≥ 0, Product of roots > 0 and
sum of roots < 0. We can say that the final answer is
m ∈ (-4, -3]