CAT Exam > CAT Questions > If a and b are integers such that 2x2- ax + 2...
Start Learning for Free
If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b is
Correct answer is '36'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 &...
Let f(x) = 2x2 - ax + 2. We can see that f(x) is a quadratic function.
For, f(x) > 0, Discriminant (D) < />
=> (-a)2 – 4*2*2< />
=> (a-4)(a+4) < />
=> a ε (-4,4)
Therefore, integer values that 'a' can take = {-3, -2, -1,0,1,2,3}
Let g(x) = x2- bx + 8. We can see that g(x) is also a quadratic function.
For, g(x)≥0, Discriminant (D) ≤ 0
=> (-b)2– 4*8* 1 < />
=>(b - √32 ) (b + √32 ) < />
=> b ε(-√32 ,√32 )
Therefore, integer values that 'b' can take = {-5, -4, -3, -2, -1,0,1,2,-3,4,5}
We have to find out the largest possible value of 2a - 6b.
The largest possible value will occur when 'a' is maximum and 'b' is minimum.
amax = 3, bmin = -5
Therefore, the largest possible value of 2a - 6b – 2*3 – 6*(-5) = 36.
Most Upvoted Answer
If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 &...
It seems like the equation you provided is incomplete. Could you please provide the full equation so that I can assist you further?
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b isCorrect answer is '36'. Can you explain this answer?
Question Description
If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b isCorrect answer is '36'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b isCorrect answer is '36'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b isCorrect answer is '36'. Can you explain this answer?.
If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b isCorrect answer is '36'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b isCorrect answer is '36'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b isCorrect answer is '36'. Can you explain this answer?.
Solutions for If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b isCorrect answer is '36'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b isCorrect answer is '36'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b isCorrect answer is '36'. Can you explain this answer?, a detailed solution for If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b isCorrect answer is '36'. Can you explain this answer? has been provided alongside types of If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b isCorrect answer is '36'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If a and b are integers such that 2x2- ax + 2 > 0 and x2 - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b isCorrect answer is '36'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup