CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

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

Video Explanation

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.