CAT Practice : Inequalities

You are here: Home  CAT Questionbank   CAT Quant  Algebra: Inequalities  Question 21
Show this question to anyone who says you need differentiation to crack an MBA

Inequalities - Minimum Value

    Q.21:What is the minimum value of f(x) = x2 – 5x + 41?


  • Correct Answer
    Choice A.

Detailed Solution

This question is present for one reason and one reason only. To talk about the idea of “completion of squares”. There are two ways of solving this question

The ugly differentiation based method and the beautiful completion of squares method.

Always pick the elegant method. You might not prefer VVS Laxman over Gary Kirsten, or Federer over Nadal. But these are matters of sport. When it comes to math solutions – elegant solutions kick ass every time.

What is this famous completion of squares method ? Any quadratic expression of the form x2 + px + q can be written in the form (x +a)2 + b.

Write in that form, enjoy the equation and have some fun.

x2 – 5x + 41 = (x + a)2 + b. what value should ‘a’ take? Forget about b for the time being.

(x + a)2 = x2 + 2ax + a2. The 2ax term should correspond to -5x. Done and dusted.

a = . a2 =

x2 – 5x + 41 can be written as x2 – 5x + + 41 = (x – )2 + 41 –

= (x – )2 +

The minimum value this expression can take is .

Correct Answer: B.

Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.

Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play

More questions from Inequalities

  1. Inequalities - Integer Solutions
  2. Cubic Inequalities
  3. Quadratic Inequalities
  4. Integer Roots - Trial and Error
  5. Modulus Inequalities
  6. Natural Numbers
  7. Integers - Polynomials
  8. Modulus - Quadratic
  9. Quadratic Inequalities
  10. Inequalities - Integer Solutions
  11. Modulus - Tricky Question
  12. Maximum Possible Value
  13. Inequalities - Integer solutions
  14. Maximum Possible Value
Inequalities are crucial to understand many topics that are tested in the CAT. Having a good foundation in this subject will make us tackling questions in Coordinate Geometry, Functions, and most importantly in Algebra much more comfortable.