JEE Exam > JEE Questions > If both roots of the quadratic equation(2 &nd...
Start Learning for Free
If both roots of the quadratic equation
(2 – x) (x + 1) = p are distinct & positive, then p must lie in the interval
- a)(2, ¥)
- b)(2, 9/4)
- c)(–¥, –2)
- d)(–¥, ¥)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If both roots of the quadratic equation(2 –x) (x + 1) = p are di...
This question is part of UPSC exam. View all JEE courses
Most Upvoted Answer
If both roots of the quadratic equation(2 –x) (x + 1) = p are di...
If both roots of the quadratic equation are equal, then the discriminant, denoted as Δ, must be equal to zero. The discriminant is given by the formula Δ = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
In this case, since both roots are equal, we can write the quadratic equation as (x - r)(x - r) = 0, where r is the common root.
Expanding this equation, we have x^2 - 2rx + r^2 = 0.
Comparing this with the standard form of a quadratic equation, we can see that a = 1, b = -2r, and c = r^2.
Substituting these values into the discriminant formula, we get Δ = (-2r)^2 - 4(1)(r^2).
Simplifying this expression, we have Δ = 4r^2 - 4r^2 = 0.
Therefore, if both roots of the quadratic equation are equal, the discriminant will be equal to zero.
In this case, since both roots are equal, we can write the quadratic equation as (x - r)(x - r) = 0, where r is the common root.
Expanding this equation, we have x^2 - 2rx + r^2 = 0.
Comparing this with the standard form of a quadratic equation, we can see that a = 1, b = -2r, and c = r^2.
Substituting these values into the discriminant formula, we get Δ = (-2r)^2 - 4(1)(r^2).
Simplifying this expression, we have Δ = 4r^2 - 4r^2 = 0.
Therefore, if both roots of the quadratic equation are equal, the discriminant will be equal to zero.
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 both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. Can you explain this answer?
Question Description
If both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. 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 both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. 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 both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. Can you explain this answer?.
If both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. 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 both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. 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 both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. Can you explain this answer?.
Solutions for If both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. 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 both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. Can you explain this answer?, a detailed solution for If both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of If both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If both roots of the quadratic equation(2 –x) (x + 1) = p are distinct & positive, then p must lie in the intervala)(2, ¥)b)(2, 9/4)c)(–¥, –2)d)(–¥, ¥)Correct answer is option 'B'. 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