The best questions to practice for CAT Exam are the actual CAT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. If you would like to take the same inside a testing engine (for **Free**) head out here: **CAT Official Question Mocks**. In CAT 2017 we saw some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts. Original CAT Question paper is the best place to start off your CAT prep practice. This page provides exactly that. To check out about 1000 CAT Level questions with detailed video solutions for free, go here: **CAT Question Bank**

Question 27 : If f_{1}(x) = x^{2} + 11x + n and f_{2}(x) = x, then the largest positive integer n for which the equation f_{1}(x) = f_{2}(x) has two distinct real roots, is : [TITA]

Buy CAT'21 95-99 Booster Course for just

Valid until 19th Sep

Online Batches Available Now!

Given that f_{1}(x) = x^{2} + 11x + n and f_{2}(x) = x,

Then we have to find the largest positive integer n for which the equation f_{1}(x) = f_{2}(x) has two distinct real roots.

⟹ x^{2} + 11x + n = x

⟹ x^{2} + 11x – x + n = 0

⟹ x^{2} + 10n + n = 0

The discriminant should be greater than zero, D > 0.

So, b^{2} – 4ac > 0.

⟹ 10^{2} – 4n > 0

⟹ 100 – 4n > 0

⟹ 25 – n > 0

⟹ n = 24

Hence if f_{1}(x) = x^{2} + 11x + n and f_{2}(x) = x, then the largest positive integer n for which the equation

f_{1}(x) = f_{2} (x) has two distinct real roots, is 24.

The question is **"If f _{1}(x) = x^{2} + 11x + n and f_{2}(x) = x, then the largest positive integer n for which the equation f_{1}(x) = f_{2}(x) has two distinct real roots, is : [TITA]" **

CAT 2021

Enroll at

44,000/-

Online Classroom Batches Starting Now!

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484 / 94459 38484

**WhatsApp:** WhatsApp Now

**Email: **info@2iim.com