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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

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Explanatory Answer

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.

 

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