CAT 2020 Linear and Quadratic Equations Question (Hard)

Question

Let f x x ax b and g x f x 1 - f x - 1 . If f x 0 for all real x, and g 20 72, then the smallest possible value of b is

Accepted Answer

Step 1 Given f x x ax b g x f x 1 f x 1 Compute g x f x 1 x 1 a x 1 b x 2x 1 ax a b f x 1 x 1 a x 1 b x 2x 1 ax a b Now subtract g x f x 1 f x 1 x 2x 1 ax a b x 2x 1 ax a b x x 2x 2x ax ax a a b b 1 1 4x 2a So, g x 4x 2a Step 2 We are given g 20 72 So, 4 20 2a 72 80 2a 72 2a 8 a 4 Now f x x 4x b We

CAT 2020

Quantitative

Linear and Quadratic Equations

Hard

Let f(x) = x² + ax + b and g(x) = f(x + 1) - f(x - 1). If f(x) ≥ 0 for all real x, and g(20) = 72, then the smallest possible value of b is

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