### CAT - Inequalities

**Question:**

Solve
the inequality x

^{3}– 5x^{2}+ 8x – 4 > 0.
A. (2, )

B. (1, 2) U (2, )

C. (-, 1) U (2, )

D. (-, 1)

**Correct Answer : (B)**

**Explanation:**

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 black box is a +ve number,
the solution is as follows:

1 < x < 2 OR x > 2

**Answer Choice (B)**

**Difficulty level 2**

Labels: CAT 2013 questions, CAT Coaching classes, CAT Coaching classes Chennai, CAT Inequalities, CAT questions, CAT Solutions

## 0 Comments:

Post a Comment

Subscribe to Post Comments [Atom]

<< Home