Question

Solve for x: $x^2$ - x - 6 > 0

• A. (-2, 3)
• B. [-2, 3]
• C. (-∞, -2] ∪ [3, ∞)
• D. (-∞, -2) ∪ (3, ∞)

Answer 1

The correct option is D

(-∞, -2) ∪ (3, ∞)

$x^2$ - x - 6 > 0 $\Rightarrow$ (x + 2) (x - 3) > 0

Now $x^2$ - x - 6 = 0 $\Rightarrow$ x = -2,3

Now, on number line mark x = -2 and x = 3

(i) Now when x > 3, x - 3 > 0 and x + 2 > 0

$\Rightarrow$ (x + 2) (x - 3) > 0 ------------(1)

(ii)When -2< x <3,x + 2 > 0 but x - 3 < 0

$\Rightarrow$ (x + 2) (x - 3) < 0 ------------(2)

(iii)When x < -2,x + 2 < 0 and also x - 3 < 0

$\Rightarrow$ (x + 2) (x - 3) > 0 ------------(3)

From (1),(2) and (3), the sign scheme of given expression $x^2$ - x - 6 is

So, $x^2$ - x - 6 > 0 for x ∈ ($-\infty$,-2) U (3,$\infty$)

At x = -2 and x = 3, $x^2$ - x - 6 = 0. So,we don't include those values.