For which of the following values of K, does the equation |x2 – 12x + 32| = K have exactly four roots? a) 0 b)2 c)4 d)6

Ans. b)2
|x2 - 12x + 32| = K can be written as x2 - 12x + 32 = +/- K For 4 solutions, the value of B^2 - 4AC should be positive for both +/- K. Only valid in case of 2.
K = 0 has only 2 real roots
K = 4 has only 3 real roots
K = 8 has 2 real and 2 imaginary roots