**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**

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