CAT 2018 Linear and Quadratic Equations Question (Hard)

Question

If and are integers such that and for all real numbers , then the largest possible value of is TITA

Accepted Answer

Step 1 We are given two quadratic inequalities 1. for all real . 2. for all real . For a quadratic expression to be always positive or non-negative, its discriminant must be negative or zero, respectively. Step 2 For the inequality , the discriminant is Delta_1 a 2 - 4 times 2 times 2 a 2 - 16 For t

CAT 2018

Quantitative

Linear and Quadratic Equations

Hard

If $a$ and $b$ are integers such that $2x^2 - ax + 2 > 0$ and $x^2 - bx + 8 \geq 0$ for all real numbers $x$ , then the largest possible value of $2a - 6b$ is [TITA]

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