CAT Quantitative Aptitude Questions | CAT Algebra - Inequalities questions

CAT Questions | Algebra | Inequalities - Cubic Inequalities

The question is about finding the solution of a cubic inequality. Our task is to find the solution of the cubic inequality. Inequalities are crucial to understand many topics that are tested in the CAT exam. Having a good foundation in this subject can help us tackle questions in Coordinate Geometry, Functions, and most importantly in Algebra. A range of CAT questions can be asked based on this simple concept.

Question 2: Solve the inequality x3 – 5x2 + 8x – 4 > 0.

  1. (2, ∞)
  2. (1, 2) ∪ (2, ∞)
  3. (-∞, 1) ∪ (2, ∞)
  4. (-∞, 1)

Online CAT Coaching for CAT 2019


Signup to sample the Best CAT Online Coaching


Best CAT Coaching in Chennai


Starts Sat, Mar 16, 2019


Explanatory Answer

Method of solving this CAT Question from Algebra - Inequalities : We all know (or should soon) how to solve a quadratic inequality. How about a cubic? Try to see if you can factorise the equation, and see how the equation behaves around the roots.

Let a, b, c be the roots of this cubic equation
a + b + c = 5
ab + bc + ca = 8
abc = 4
This happens when a = 1, b = 2 and c = 2 {This is another approach to solving cubic equations}.

The other approach is to use polynomial remainder theorem
If you notice, sum of the coefficients = 0
=> P(1) = 0
=> (x - 1) is a factor of the equation. Once we find one factor, we can find the other two by dividing the polynomial by (x - 1) and then factorizing the resulting quadratic equation.
(x - 1) (x - 2) (x - 2) > 0

Let us call the product (x - 1) (x - 2) (x - 2) as a black box.
If x is less than 1, the black box is a –ve number
If x is between 1 and 2, the black box is a +ve number
If x is greater than 2, the black box is a +ve number

Since we are searching for the regions where the black box is a +ve number, the solution is as follows: 1 < x < 2 OR x > 2

The question is "Solve the inequality x3 – 5x2 + 8x – 4 > 0."

Hence the answer is "(1, 2) ∪ (2, ∞)"

Choice B is the correct answer.

Online CAT Coaching
Try it free!

Register in 2 easy steps and start learning in 30 seconds!

★ Sign up for Free

Already have an Account?

★ Login to Continue

CAT Coaching in Chennai

Next Weekend Batch Starts Sat, Mar 23rd, 2019

★ CAT Coaching Info

Best CAT Coaching in Chennai

Sign up for a Free Demo of our CAT Coaching in Chennai

★ Schedule Demo


CAT Online Preparation | CAT Algebra Videos On YouTube


Other useful sources for Algebra Questions | Inequalities Sample Questions


CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
10-C, Kalinga Colony, Bobbili Raja Salai
K.K.Nagar, Chennai. India. Pin - 600 078

How to reach 2IIM?

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