Question

If x ∈ Z (set of integers) such that x2 – 3x – 4 < 0. Then number of possible values of x is

Answer 1

x2 - 4x + x -4 < 0

(x-4)(x+1)<0

so x=4 and -1

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Answer 2

Given:

$x$ ∈ $Z$ such that $x^2-3x-4 < 0$

To Find:

The number of possible values of $x$.

Solution:

We are given the inequation $x^2-3x-4 < 0$.

Let us find the factors of the left-hand side expression

  $x^2-3x-4$

$=x^2-4x+x-4$

$=(x+1)(x-4)$

So the expression changes its sign at two points: -1 and 4

To have the value less than 0, only one of them will have to be negative at a time.

This is possible if $x < -1$ & $x > 4$ or $x > -1$ & $x < 4$

Since $x$ cannot be less than -1 and greater than 4 at the same time, the possible integral values of $x$ are 0, 1, 2, and 3.

Hence, the possible values of $x$ are 0, 1, 2, and 3.

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