Q. 18

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

A. (,3] [5, )

B. [3, 5]

C. (4, 3]

D. (3, 1]

Answer :

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]

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive Quiz on Quadratic EquationsInteractive Quiz on Quadratic EquationsInteractive Quiz on Quadratic Equations73 mins
Interactive Quiz on Quadratic Equations-02Interactive Quiz on Quadratic Equations-02Interactive Quiz on Quadratic Equations-0252 mins
1 Hour- 1 Chapter | Quadratic Equations1 Hour- 1 Chapter | Quadratic Equations1 Hour- 1 Chapter | Quadratic Equations61 mins
Challenging Quiz on Quadratic Equations | Test YourselfChallenging Quiz on Quadratic Equations | Test YourselfChallenging Quiz on Quadratic Equations | Test Yourself55 mins
Relationship b/w coefficients & roots | Quadratic EquationRelationship b/w coefficients & roots | Quadratic EquationRelationship b/w coefficients & roots | Quadratic Equation42 mins
Practise Questions General Solution of Trigonometric Equations with RHS as 0, 1 or -1Practise Questions General Solution of Trigonometric Equations with RHS as 0, 1 or -1Practise Questions General Solution of Trigonometric Equations with RHS as 0, 1 or -133 mins
How to find General Solution of Trigonometric Equations with RHS as 0, 1 or -1How to find General Solution of Trigonometric Equations with RHS as 0, 1 or -1How to find General Solution of Trigonometric Equations with RHS as 0, 1 or -136 mins
Parametric Equations of Straight lineParametric Equations of Straight lineParametric Equations of Straight line48 mins
Interactive Quiz on Equations & inequationsInteractive Quiz on Equations & inequationsInteractive Quiz on Equations & inequations63 mins
Interactive Quiz on Equations of lineInteractive Quiz on Equations of lineInteractive Quiz on Equations of line23 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses