CAT 2017 Question Paper | Quants Slot 2

CAT Previous Year Paper | CAT Quadratic Equations Questions | Question 24

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 24 : The minimum possible value of the sum of the squares of the roots of the equation x2 + (a + 3)x - (a + 5) = 0 is

  1. 1
  2. 2
  3. 3
  4. 4

2IIM : Best Online CAT Coaching


2IIM's Online CAT Coaching
Get CAT Last Mile Prep Course for 799 /-
CAT Online Coaching


Video Explanation


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2020
Starts Sat, November 2nd, 2019


Explanatory Answer

Method of solving this CAT Question from Quadratic Equations

Let p and q be two roots of the equation
We have to find the minimum value of (p2 + q2)
p2 + q2 = (p + q)2 โ€“ 2pq ----(i)
Sum of the roots = \\frac{โˆ’๐‘}{๐‘Ž}).
Therefore, p + q = -(a + 3)
Product of the roots = \\frac{c}{๐‘Ž})
Therefore, pq = -(a + 5)
Substituting these values back in (i)
p2 + q2 = [(-a + 3)2 โ€“ 2(-a + 5)]
p2 + q2 = a2 + 6a + 9 + 2a + 10
p2 + q2 = a2 + 8a + 19
We have to find the minimum value of a2 + 8a + 19.
By completion of squares, 19 can be split into 16 and 3
โŸน a2 + 8a + 16 + 3
โŸน (a + 4)2 + 3
The minimum possible value is 3 when a = -4.

The question is "The minimum possible value of the sum of the squares of the roots of the equation x2 + (a + 3)x - (a + 5) = 0 is"

Hence, the answer is 3

Choice C is the correct answer

ย 

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


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
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com