# CAT 2019 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Quants Questions | Question 31

Quadratic equation is one of the tougher chapters in CAT syllabus. While it should definitely be included in your CAT Preparation plan, the topic is vast and the questions are often tough. Hence it is prudent to prepare quadratic equations only if you are having an early start for your CAT Preparation.

Question 31 : The product of the distinct roots of |x2 - x - 6| = x + 2 is

1. -4
2. -16
3. -8
4. -24

## Best CAT Coaching in Chennai

#### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now!

Given that ∣x2 - x - 6∣ = x + 2
Removing the modulus,
(x2 - x - 6) = x + 2 (or) -(x2 - x - 6) = x + 2
Solving (x2 - x - 6) = x + 2
We get, x2 - 2x - 8 = 0
(x-4) (x+2) = 0
x = 4 or -2
For the solution to be valid, the value of the equation must be positive
When x = 4,
x2 - x - 6 = x +2
16 - 4 -6 = x + 2
6 - 2 = x
4 = x. Therefore, x = 4 works
For x = -2,
x2 - x - 6 = x +2
4 + 2 - 6 = x + 2
0 - 2 = x
-2 = x. Therefore, x = - 2 works
Similarly, Solving -(x2 - x - 6) = x + 2
-x2 + x + 6 = x + 2
x2 = 4
x = +2 or -2
For the solution to be valid, x2 - x - 6 must be negative
When x = +2,
-x2 + x + 6 = x +2
-4 + 2 + 6 = x + 2
+ 2 = x Therefore, x = 2 works.
Therefore, Product of distinct roots = 2 x -2 x 4 = -16

The question is "The product of the distinct roots of |x2 - x - 6| = x + 2 is "

##### Hence, the answer is -16

Choice B is the correct answer.

###### CAT Coaching in ChennaiCAT 2023

Classroom Batches Starting Now! @Gopalapuram

###### Best CAT Coaching in Chennai Introductory offer of 5000/-

Attend a Demo Class

##### 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?

Mobile: (91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com