Linear and Quadratic Equations

You are here: Home  CAT Questionbank   CAT Quant  Linear & Quad. Eqns.  Question 5

Counting - Quadratic Equations

    x2 - 9x + |k| = 0 has real roots. How many integer values can 'k' take?
    1. 40
    2. 21
    3. 20
    4. 41

 

  • Correct Answer
    Choice D. 41

Explanatory Answer

Click to watch video solution
Click to view the explanation as a slide show

Detailed Solution

Discriminant, D = 81 – 4|k|
If roots are real, D > 0
81 – 4|k| > 0
4|k| < 81
|k| < 20.25

Hence, –20.25 < k < 20.25
The integer values that k can take are –20, –19, –18 … 0 … 18, 19 and 20.

41 different values (Remember to include 0. Answer choice 'A' will definitely be 40

Correct Answer: 41.



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.