Handa Ka Funda
CAT 2021
GK
DM
SBI PO
IBPS PO
Mocks
Demo Videos
Blog
CAT Syllabus
Free Downloads
Past Results
Graduation
Quantitative Aptitude – Algebra – Quadratic Equations – If a and b are integers such that 2x^2
Slot -2 – Quantitative Aptitude – Algebra – Quadratic Equations – If a and b are integers such that 2x^2
If a and b are integers such that 2x^2 −ax + 2 > 0 and x^2 −bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a−6b is?
Answer:
36
Solution:
Given,
2x^2 −ax + 2 > 0
2{ (x-a/4)^2 – a^2/16+1} > 0 ∀ x ∈R
-a^2/16+1 > 0
a ∈{ -3,-2,-1,0,1,2,3}
x^2 −bx + 8 ≥ 0
(x-b/2)^2 – b^2 /4 + 8>0 ∀ x ∈R -b^2 /4 + 8>0
b ∈{-5,-4,-3,-2,-1,0,1,2,3,4,5 }
So largest possible value of 2a – 6b = 3*2 – 6(-5) = 36
Other posts related to Quantitative Aptitude – Modern Maths
Permutation and Combination – Fundamental Principle of Counting
Permutation and Combination – Distribution of Objects
How to find Rank of a Word in Dictionary (With or Without Repetition)
Set Theory- Maximum and Minimum Values
How to solve questions based on At least n in Set Theory for CAT Exam?
Sequence and Series Problems and Concepts for CAT 2017 Exam Preparation
Basic Probability Concepts for CAT Preparation
WhatsApp
Join our broadcast list for important updates
Telegram
Join our group for important updates
Crack CAT with Unacademy!
Use referral code
HANDA
to get 10% off.
Daily Live Classes
Live Tests and Quizzes
Structured Courses
Personalized Coaching
Enroll Now
Download Unacademy App
New message
×
Got a discount code?
Submit
Name
Email *
Please provide your email.
Phone Number *
Please provide your phone number.
State *
Reference
Close
Pay