# CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

###### CAT Questions | Algebra | Inequalities - Minimum Value CAT Questions

The question is about minimizing a function. Our task is to find out the minimum value of a quadratic function. Do we need calculus for that? Inequalities are crucial to understand many topics that are tested in the CAT exam. Having a good foundation in this subject can help us tackle questions in Coordinate Geometry, Functions, and most importantly in Algebra. A range of CAT questions can be asked based on this simple concept.

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

1. $$frac{139}{4}\\$ 2. $\frac{149}{4}\\$ 3. $\frac{129}{4}\\$ 4. $\frac{119}{4}\\$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2021Online Batches Available Now! ### Explanatory Answer ##### Method of solving this CAT Question from Algebra - Inequalities : Show this question to anyone who says you need differentiation to crack CAT exam. 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 =$$frac{-5}{2}\\$a2 = $\frac{25}{4}\\$ x2 – 5x + 41 can be written as x2 – 5x + $\frac{25}{4}\\$ – $\frac{25}{4}\\$ + 41 = x – $\frac{5}{2}\\$2 + 41 – $\frac{25}{4}\\$ = x – $\frac{5}{2}\\$2 + $\frac{139}{4}\\$ The minimum value this expression can take is $\frac{139}{4}\\$ The question is "What is the minimum value of f$x) = x2 – 5x + 41?"

##### Hence the answer is "$$frac{139}{4}\\$" Choice A is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in ChennaiPrices slashed by Rs 4000/- Attend a Demo Class ## CAT Online Preparation | CAT Algebra Videos On YouTube #### Other useful sources for Algebra Questions | Inequalities Sample Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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