CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

CAT Questions | Algebra | Polynomials - Roots

The question is about finding roots of a cubic equation. This question becomes easy once you find out the product of the roots using given details. Polynomials is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept.

Question 9: x3 – 18x2 + bx – c = 0 has positive real roots, p, q and z. If geometric mean of the roots is 6, find b.

  1. 36
  2. -216
  3. 108
  4. -72

Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!


2IIM : Best Online CAT Coaching.


Video Explanation


Best CAT Coaching in Chennai


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


Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Polynomials: How is GM related to the product of the roots?

p + q + z = 18
pq + qz + zp = b
pqz = c
According to the question, (pqz)1/3 = 6. Hence, pqz = c = 216.
This is possible only when p = q= z = 6. {Arithmetic mean of p, q and z = 6, GM is also 6. This is possible only when all three numbers are equal.}
So, pq + qz + zp = 36 * 3 = 108 = b.
Hence, b = 108.

The question is "x3 – 18x2 + bx – c = 0 has positive real roots, p, q and z. If geometric mean of the roots is 6, find b."

Hence the answer is "108"

Choice C is the correct answer.

 


CAT Online Coaching | CAT Algebra Videos On YouTube


Other useful sources for Algebra Questions | Polynomials 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,
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