Quantitative Aptitude – Algebra – Quadratic Equations – If a and b are integers such that 2x^2


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

Online Coaching Course for CAT 2020

a) 900+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video