# CAT Quantitative Aptitude Questions | CAT Algebra - Linear Equations; Quadratic Equations

###### CAT Questions | Algebra | Quadratic Equations - Counting CAT Questions

The question is about finding possible values of the constant in a Quadratic Equation. We need to find out the no. of values 'k' can take when the given quadratic equations has real roots. Framing and solving equations is an integral part of Linear Equations and Quadratic Equations. Get as much practice as you can in these two topics because the benefits of being good at framing equations will be useful in other concepts.

Question 5: x2 - 9x + |k| = 0 has real roots. How many integer values can 'k' take?

1. 40
2. 21
3. 20
4. 41

## Best CAT Coaching in Chennai

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

##### Method of solving this CAT Question from CAT Algebra - Quadratic Equations: Counting question with modulus also thrown in. Worry about all those negative possibilities as well.

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.)

The question is "x2 - 9x + |k| = 0 has real roots. How many integer values can 'k' take?"

##### Hence the answer is "41"

Choice D is the correct answer.

###### CAT Coaching in ChennaiCAT 2022

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?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com