CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

CAT Questions | Algebra | Polynomials - Cubic Equation

The question is about Cubic Equation. Sum and product of roots of a polynomial and two roots are given and we need to find out an algebraic term of the roots. 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 20:x3 – 4x2 + mx – 2 = 0 has 3 positive roots, two of which are p and \\frac{1}{p}\\) Find m.

  1. 5
  2. -11
  3. 8
  4. -2

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Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Polynomials: Relate the given roots and the product and you will be through!

Let the roots be p, \\frac{1}{p}\\) and q.
p * \\frac{1}{p}\\) * q = 2
So, the 3rd root = q = 2
p + \\frac{1}{p}\\) + 2 = 4
p + \\frac{1}{p}\\) = 2 {For any real p |p + \\frac{1}{p}\\) > 2| }
p2 – 2p + 1 = 0
(p – 1)2 = 0. Hence, p is 1.
The roots are 1, 1 and 2.
(1 * 1) + (1 * 2) + (1 * 2) = 5 = m

The question is "x3 – 4x2 + mx – 2 = 0 has 3 positive roots, two of which are p and \\frac{1}{p}\\) Find m."

Hence the answer is "5"

Choice A is the correct answer.

 


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