JEE Main · 2021 · 16 Mar 2021 · Shift 1 · Basic Mathematics

The number of elements in the set

{x \in R : (∣ x ∣ - 3) ∣ x + 4∣ = 6}

is equal to :

Answer: (D)

Solution

Consider cases based on the sign of

x

. For

x \geq 0

(x - 3) (x + 4) = 6

gives

x^{2} + x - 18 = 0

, so

x = \frac{- 1 + 73}{2}

(positive root). For

- 4 \leq x < 0

(- x - 3) (x + 4) = 6

gives

- x^{2} - 7 x - 12 = 6

, so

x^{2} + 7 x + 18 = 0

(no real roots). For

x < - 4

(- x - 3) (- x - 4) = 6

gives

x^{2} + 7 x + 6 = 0

, so

x = - 1

x = - 6

. Only

x = - 6

satisfies

x < - 4

. Thus there are 2 solutions.

JEE Main · 2021 · 16 Mar 2021 · Shift 1 · Single correct option