JEE Exam > JEE Questions > If the difference between the roots of the eq...
Start Learning for Free
If the difference between the roots of the equation x2 + ax + 1 = 0 is less than √5, then the set of possible values of a is
- a)(–3, –2] ∪ [2, 3)
- b)(–3, ∞)
- c)(3, ∞)
- d)(–∞, 3)
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If the difference between the roots of the equation x2+ ax + 1 = 0 is ...
Most Upvoted Answer
If the difference between the roots of the equation x2+ ax + 1 = 0 is ...
The difference between the roots of a quadratic equation can be found using the discriminant. For the equation x^2 + ax + 1 = 0, the discriminant is given by b^2 - 4ac, where a = 1, b = a, and c = 1.
So, the discriminant is a^2 - 4(1)(1) = a^2 - 4.
If the difference between the roots is less than a, then the discriminant must be positive and less than a^2.
Therefore, a^2 - 4 > 0 and a^2 - 4 < a^2.="" />
Simplifying the inequalities, we have:
a^2 > 4 and -4 < 0.="" />
The first inequality, a^2 > 4, implies that a > 2 or a < -2.="" />
The second inequality, -4 < 0,="" is="" always="" true.="" />
So, the difference between the roots of the equation x^2 + ax + 1 = 0 is less than a if a > 2 or a < -2.="" />
So, the discriminant is a^2 - 4(1)(1) = a^2 - 4.
If the difference between the roots is less than a, then the discriminant must be positive and less than a^2.
Therefore, a^2 - 4 > 0 and a^2 - 4 < a^2.="" />
Simplifying the inequalities, we have:
a^2 > 4 and -4 < 0.="" />
The first inequality, a^2 > 4, implies that a > 2 or a < -2.="" />
The second inequality, -4 < 0,="" is="" always="" true.="" />
So, the difference between the roots of the equation x^2 + ax + 1 = 0 is less than a if a > 2 or a < -2.="" />
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer?
Question Description
If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer?.
If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer?.
Solutions for If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the difference between the roots of the equation x2+ ax + 1 = 0 is less than√5, then the set of possible values of a isa)(–3, –2] ∪ [2, 3)b)(–3, ∞)c)(3, ∞)d)(–∞, 3)Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup