Linear and Quadratic Equations

You are here: Home  CAT Questionbank   CAT Quant  Linear & Quad. Eqns.  Question 12
How many solutions are there for this quadratic equation containing modulus?

Real and imaginary solutions for an equation

    How many real solutions are there for the equation x2 – 7|x| - 30 = 0?
    1. 3
    2. 1
    3. 2
    4. none

 

  • Correct Answer
    Choice C. 2

Detailed Solution

Case 1: x > 0
x2 – 7x - 30 = 0
( x - 10 ) ( x - 3 ) = 0
X = 10, x = -3
But x = -3 is not possible as we have considered x > 0, thus 1 solution for this case.
Case 2: x < 0
x2 + 7x - 30 = 0
( x + 10 )( x - 3)=0
X = -10 and x = 3
Only x = -10 is permissible.
Thus this equation has 2 real solutions
Alternatively, we can think of the above as a quadratic in |x|
x2 – 7|x| - 30 = 0 can be factorized as
(|x| -10) ( |x| + 3) = 0
|x| cannot be -3, |x| can only be 10. X can take 2 real values.


Correct Answer: 2



Our Online Course, Now on Google Playstore!

2IIM's App

Fully Functional Course on Mobile

All features of the online course, including the classes, discussion board, quizes and more, on a mobile platform.


Cache Content for Offline Viewing

Download videos onto your mobile so you can learn on the fly, even when the network gets choppy!

Get it on Google Play
Visit Piverb.com
Visit Wizako.com

More Questions from Linear & Quad. Equations

  1. Integer Values; Modulus
  2. Integer Values; Modulus
  3. Integer Values; Modulus
  4. Quadratic Discriminant
  5. Quadratic Discriminant
  6. Quadratics - Counting
  7. Integer Solutions
  8. Linear Equations - Median
  9. Condition for Unique Soln.
Solving equations well is an integral part to cracking any competitive exam. Get cartloads of practice on these two topics.