Given x2 - 3 |x| + 2 = 0 ... (i) We have to find the number of real solutions of the equation (i). Considering two cases using definition of modulus function 1. x > 0 for x > 0 , |x| = x ⇒ x2 - 3x + 2 = 0 [Using quadratic equation (i)] ⇒ (x - 1) (x - 2) = 0 ⇒ x = 1 , 2 2. x ≤ 0 for x ≤ 0 , |x| = - x ⇒ x2 + 3x + 2 = 0 ⇒ (x + 1) (x + 2) = 0 ⇒ x = - 1 , - 2 ∴ Number of real solutions of the quadratic equation (i) = 4 Hence, option 'B' is correct